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296 relations: *-algebra, + h.c., Abelian variety of CM-type, Absolute value, Adjoint filter, Advanced wave, AKNS system, Algebraic number field, Algebraic number theory, All-pass filter, Almost complex manifold, Ambiguity function, Analytic function, Analytic signal, Antenna (radio), Antiholomorphic function, Antilinear map, Antiunitary operator, Area theorem (conformal mapping), Arity, Asterisk, Autocorrelation, Automorphism, Étale cohomology, Bairstow's method, Banach space, Berezin transform, Bessel filter, Biconjugate gradient method, Biquaternion, Blaschke product, Born rule, Boy's surface, Bra–ket notation, Bring radical, Bures metric, C mathematical functions, Cartan decomposition, Casio fx-3650P, Casus irreducibilis, Cauchy–Riemann equations, Cauchy–Schwarz inequality, Cayley–Dickson construction, CC, Characteristic equation (calculus), Characteristic function (probability theory), Circular section, CM-field, Cnoidal wave, Collineation, ..., Compass-and-straightedge construction, Completing the square, Complex conjugate line, Complex conjugate root theorem, Complex conjugate vector space, Complex number, Complex random variable, Complex random vector, Complexification, Conformal map, Conic section, Conj, Conjugate (square roots), Conjugate transpose, Conjugation, Continuity equation, Continuous functions on a compact Hausdorff space, Continuous wavelet transform, Courant bracket, Covariance matrix, Cross-correlation, Cross-covariance, Cube root, Cubic function, Cyclostationary process, Damping ratio, De Rham curve, Determinant, Dianalytic manifold, Difference of two squares, Diffraction formalism, Digital image correlation and tracking, Dihedral group, Dirichlet's unit theorem, Discrete Fourier transform, Discrete-time Fourier transform, Discriminant, Division algebra, Division ring, Dold manifold, Dot product, Durand–Kerner method, Edmund Schuster, Eigenfunction, Eigenvalues and eigenvectors, Eisenstein integer, Eisenstein prime, Emmy Noether, Entire function, Error function, Euler's rotation theorem, Fabry–Pérot interferometer, Factorization, Field of definition, Four-vector, Fourier transform, Fraunhofer diffraction equation, Fredholm's theorem, Free particle, Fresnel equations, Frobenius inner product, Fubini–Study metric, Galois group, Gauss sum, Gaussian beam, Gaussian rational, Generalised circle, Generalized complex structure, Generalized dihedral group, Generalized Fourier series, Geometry of roots of real polynomials, Glossary of field theory, Gluon field, Group of Lie type, Hamiltonian (quantum mechanics), Harmonic wavelet transform, Hölder's inequality, Hermitian adjoint, Hermitian function, Hermitian matrix, Hilbert C*-module, Hilbert space, History of Lorentz transformations, Hodge theory, Holomorphic function, Hopf bifurcation, Hopf fibration, Hyperelliptic curve cryptography, Imaginary point, Imaginary unit, Impedance bridging, Impedance matching, Index of electrical engineering articles, Inner product space, Input impedance, Invariant (mathematics), Inversive geometry, Involution (mathematics), IQ imbalance, ISO 31-11, Isomorphism, Isosceles triangle, Jordan normal form, Joule heating, K-space (magnetic resonance imaging), Klein bottle, Klein–Gordon equation, Koopman–von Neumann classical mechanics, Kutta–Joukowski theorem, Lagrange's identity, Laplace transform, LC circuit, Least-squares function approximation, Line integral, Linear algebra, Linear complex structure, Linear difference equation, Linear differential equation, Linear map, List of character tables for chemically important 3D point groups, List of equations in quantum mechanics, List of mathematical symbols, List of mathematical symbols by subject, Magnitude (mathematics), Majorana fermion, Matched filter, Mathematical descriptions of opacity, Matrix (mathematics), Matrix consimilarity, Matrix decomposition, Matrix mechanics, Matrix multiplication, Matrix representation of Maxwell's equations, Maximum power transfer theorem, Minimal Supersymmetric Standard Model, Minkowski space (number field), Modulational instability, Multiple-scale analysis, Multiplicative inverse, Multipliers and centralizers (Banach spaces), Negative resistance, Nested radical, Neutrino oscillation, Noether's theorem, Nondimensionalization, Nonlinear optics, Nonlinear Schrödinger equation, Normal matrix, Okubo algebra, Operator (computer programming), Orbital overlap, Orthogonal frequency-division multiplexing, Outer product, Overline, Paraboloid, Parseval's theorem, Phase correlation, Phase retrieval, Phase-shift keying, Phasor, Plane (geometry), Plane wave expansion, Polar decomposition, Polarization identity, Pole–zero plot, Positive-definite function, Power gain, Probability current, Problem of Apollonius, Progressive function, Proofs involving the Moore–Penrose inverse, Pulse compression, Q factor, Quadratic equation, Quadratic formula, Quadric, Quantization of the electromagnetic field, Quantum state, Quartic function, Quartic reciprocity, Quaternionic analysis, Rabi problem, Rayleigh's equation (fluid dynamics), Real coordinate space, Real representation, Real structure, Reality structure, Reciprocal polynomial, Reciprocity (electromagnetism), Refinable function, Representation theory of the Lorentz group, Ricci scalars (Newman–Penrose formalism), Riemann surface, Ring homomorphism, Root of unity, Rotating wave approximation, Rotation matrix, Sato–Tate conjecture, Scattering parameters, Schrödinger equation, Schwarzschild geodesics, Schwinger function, Seesaw mechanism, Sesquilinear form, Simson line, Singular point of an algebraic variety, Skew-Hermitian matrix, SL2(R), Slater-type orbital, Space–time block code, Special unitary group, Spectral density, Spectral theory, Spherical basis, Spinor, Split-quaternion, Square matrix, Square-integrable function, Staggered tuning, Standing wave ratio, Stationary phase approximation, Stokes' paradox, Stone–Weierstrass theorem, Symmetry in mathematics, Symmetry in quantum mechanics, T-symmetry, Tensor rank decomposition, Transpose, Two-dimensional conformal field theory, Uncertainty principle, Unitary group, Unitary transformation, Variance, Vector space, Vector spherical harmonics, Wave function, Wave function collapse, Wave interference, Wavelet transform modulus maxima method, Wiener deconvolution, Wirtinger derivatives, X-ray crystallography, XPIC, Z N model, Z-transform, Zero of a function. 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*-algebra
In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive rings and, where is commutative and has the structure of an associative algebra over.
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+ h.c.
+ h.c. is an abbreviation for “plus the ''H''ermitian ''c''onjugate”; it means is that there are additional terms which are the Hermitian conjugates of all of the preceding terms, and is a convenient shorthand to omit half the terms actually present.
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Abelian variety of CM-type
In mathematics, an abelian variety A defined over a field K is said to have CM-type if it has a large enough commutative subring in its endomorphism ring End(A).
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Absolute value
In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.
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Adjoint filter
In signal processing, the adjoint filter mask h^* of a filter mask h is reversed in time and the elements are complex conjugated.
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Advanced wave
Advanced wave is also referred as advanced potential, advanced field and advanced solution.
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AKNS system
In mathematics, the AKNS system is an integrable system of partial differential equations, introduced by and named after.
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Algebraic number field
In mathematics, an algebraic number field (or simply number field) F is a finite degree (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q. The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.
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Algebraic number theory
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations.
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All-pass filter
An all-pass filter is a signal processing filter that passes all frequencies equally in gain, but changes the phase relationship among various frequencies.
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Almost complex manifold
In mathematics, an almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space.
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Ambiguity function
In pulsed radar and sonar signal processing, an ambiguity function is a two-dimensional function of time delay and Doppler frequency \chi(\tau,f) showing the distortion of a returned pulse due to the receiver matched filter (commonly, but not exclusively, used in pulse compression radar) due to the Doppler shift of the return from a moving target.
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Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series.
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Analytic signal
In mathematics and signal processing, an analytic signal is a complex-valued function that has no negative frequency components.
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Antenna (radio)
In radio, an antenna is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver.
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Antiholomorphic function
In mathematics, antiholomorphic functions (also called antianalytic functions) are a family of functions closely related to but distinct from holomorphic functions.
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Antilinear map
In mathematics, a mapping f:V\to W from a complex vector space to another is said to be antilinear (or conjugate-linear) if for all a, \, b \, \in \mathbb and all x, \, y \, \in V, where \bar and \bar are the complex conjugates of a and b respectively.
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Antiunitary operator
In mathematics, an antiunitary transformation, is a bijective antilinear map between two complex Hilbert spaces such that for all x and y in H_1, where the horizontal bar represents the complex conjugate.
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Area theorem (conformal mapping)
In the mathematical theory of conformal mappings, the area theorem gives an inequality satisfied by the power series coefficients of certain conformal mappings.
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Arity
In logic, mathematics, and computer science, the arity of a function or operation is the number of arguments or operands that the function takes.
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Asterisk
An asterisk (*); from Late Latin asteriscus, from Ancient Greek ἀστερίσκος, asteriskos, "little star") is a typographical symbol or glyph. It is so called because it resembles a conventional image of a star. Computer scientists and mathematicians often vocalize it as star (as, for example, in the A* search algorithm or C*-algebra). In English, an asterisk is usually five-pointed in sans-serif typefaces, six-pointed in serif typefaces, and six- or eight-pointed when handwritten. It is often used to censor offensive words, and on the Internet, to indicate a correction to a previous message. The asterisk is derived from the need of the printers of family trees in feudal times for a symbol to indicate date of birth. The original shape was seven-armed, each arm like a teardrop shooting from the center. In computer science, the asterisk is commonly used as a wildcard character, or to denote pointers, repetition, or multiplication.
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Autocorrelation
Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay.
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Automorphism
In mathematics, an automorphism is an isomorphism from a mathematical object to itself.
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Étale cohomology
In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectures.
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Bairstow's method
In numerical analysis, Bairstow's method is an efficient algorithm for finding the roots of a real polynomial of arbitrary degree.
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Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
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Berezin transform
In mathematics — specifically, in complex analysis — the Berezin transform is an integral operator acting on functions defined on the open unit disk D of the complex plane C. Formally, for a function ƒ: D → C, the Berezin transform of ƒ is a new function Bƒ: D → C defined at a point z ∈ D by where denotes the complex conjugate of w and \mathrmA is the area measure.
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Bessel filter
In electronics and signal processing, a Bessel filter is a type of analog linear filter with a maximally flat group/phase delay (maximally linear phase response), which preserves the wave shape of filtered signals in the passband.
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Biconjugate gradient method
In mathematics, more specifically in numerical linear algebra, the biconjugate gradient method is an algorithm to solve systems of linear equations Unlike the conjugate gradient method, this algorithm does not require the matrix A to be self-adjoint, but instead one needs to perform multiplications by the conjugate transpose.
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Biquaternion
In abstract algebra, the biquaternions are the numbers, where, and are complex numbers, or variants thereof, and the elements of multiply as in the quaternion group.
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Blaschke product
In complex analysis, the Blaschke product is a bounded analytic function in the open unit disc constructed to have zeros at a (finite or infinite) sequence of prescribed complex numbers inside the unit disc.
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Born rule
The Born rule (also called the Born law, Born's rule, or Born's law) formulated by German physicist Max Born in 1926, is a law of quantum mechanics giving the probability that a measurement on a quantum system will yield a given result.
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Boy's surface
In geometry, Boy's surface is an immersion of the real projective plane in 3-dimensional space found by Werner Boy in 1901 (he discovered it on assignment from David Hilbert to prove that the projective plane could not be immersed in 3-space).
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Bra–ket notation
In quantum mechanics, bra–ket notation is a standard notation for describing quantum states.
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Bring radical
In algebra, the Bring radical or ultraradical of a real number a is the unique real root of the polynomial The Bring radical of a complex number a is either any of the five roots of the above polynomial (it is thus multi-valued), or a specific root, which is usually chosen in order that the Bring radical is a function of a, which is real-valued when a is real, and is an analytic function in a neighborhood of the real line.
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Bures metric
In mathematics, in the area of quantum information geometry, the Bures metric (named after Donald Bures) or Helstrom metric (named after Carl W. Helstrom) defines an infinitesimal distance between density matrix operators defining quantum states.
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C mathematical functions
C mathematical operations are a group of functions in the standard library of the C programming language implementing basic mathematical functions.
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Cartan decomposition
The Cartan decomposition is a decomposition of a semisimple Lie group or Lie algebra, which plays an important role in their structure theory and representation theory.
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Casio fx-3650P
Casio fx-3650P is a programmable scientific calculator manufactured by Casio Computer Co., Ltd.
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Casus irreducibilis
In algebra, casus irreducibilis (Latin for "the irreducible case") is one of the cases that may arise in attempting to solve a cubic equation with integer coefficients with roots that are expressed with radicals.
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Cauchy–Riemann equations
In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which, together with certain continuity and differentiability criteria, form a necessary and sufficient condition for a complex function to be complex differentiable, that is, holomorphic.
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Cauchy–Schwarz inequality
In mathematics, the Cauchy–Schwarz inequality, also known as the Cauchy–Bunyakovsky–Schwarz inequality, is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, vector algebra and other areas.
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Cayley–Dickson construction
In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one.
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CC
CC, cc, or C-C may refer to.
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Characteristic equation (calculus)
In mathematics, the characteristic equation (or auxiliary equation) is an algebraic equation of degree n upon which depends the solution of a given n\,th-order differential equation or difference equation.
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Characteristic function (probability theory)
In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution.
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Circular section
In geometry a circular section is a circle on a quadric surface (such as an ellipsoid or hyperboloid).
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CM-field
In mathematics, a CM-field is a particular type of number field, so named for a close connection to the theory of complex multiplication.
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Cnoidal wave
In fluid dynamics, a cnoidal wave is a nonlinear and exact periodic wave solution of the Korteweg–de Vries equation.
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Collineation
In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear.
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Compass-and-straightedge construction
Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.
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Completing the square
In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form to the form for some values of h and k. Completing the square is used in.
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Complex conjugate line
In complex geometry, the complex conjugate line of a straight line is the line that it becomes by taking the complex conjugate of each point on this line.
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Complex conjugate root theorem
In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P. It follows from this (and the fundamental theorem of algebra), that if the degree of a real polynomial is odd, it must have at least one real root.
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Complex conjugate vector space
In mathematics, the complex conjugate of a complex vector space V\, is a complex vector space \overline V, which has the same elements and additive group structure as V, but whose scalar multiplication involves conjugation of the scalars.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Complex random variable
In probability theory and statistics, complex random variables are a generalization of real-valued random variables to complex numbers, i.e. the possible values a complex random variable may take are complex numbers.
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Complex random vector
In probability theory and statistics, a complex random vector is typically a tuple of complex-valued random variables, and generally is a random variable taking values in a vector space over the field of complex numbers.
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Complexification
In mathematics, the complexification of a vector space V over the field of real numbers (a "real vector space") yields a vector space VC over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers.
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Conformal map
In mathematics, a conformal map is a function that preserves angles locally.
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Conic section
In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.
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Conj
Conj may refer to.
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Conjugate (square roots)
In mathematics, the conjugate of an expression of the form a+b\sqrt d is a-b\sqrt d, provided that \sqrt d does not appear in and.
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Conjugate transpose
In mathematics, the conjugate transpose or Hermitian transpose of an m-by-n matrix A with complex entries is the n-by-m matrix A∗ obtained from A by taking the transpose and then taking the complex conjugate of each entry.
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Conjugation
Conjugation or conjugate may refer to.
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Continuity equation
A continuity equation in physics is an equation that describes the transport of some quantity.
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Continuous functions on a compact Hausdorff space
In mathematical analysis, and especially functional analysis, a fundamental role is played by the space of continuous functions on a compact Hausdorff space with values in the real or complex numbers.
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Continuous wavelet transform
In mathematics, a continuous wavelet transform (CWT) is used to divide a continuous-time function into wavelets.
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Courant bracket
In a field of mathematics known as differential geometry, the Courant bracket is a generalization of the Lie bracket from an operation on the tangent bundle to an operation on the direct sum of the tangent bundle and the vector bundle of ''p''-forms.
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Covariance matrix
In probability theory and statistics, a covariance matrix (also known as dispersion matrix or variance–covariance matrix) is a matrix whose element in the i, j position is the covariance between the i-th and j-th elements of a random vector.
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Cross-correlation
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other.
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Cross-covariance
In probability and statistics, given two stochastic processes X.
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Cube root
In mathematics, a cube root of a number x is a number y such that y3.
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Cubic function
In algebra, a cubic function is a function of the form in which is nonzero.
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Cyclostationary process
A cyclostationary process is a signal having statistical properties that vary cyclically with time.
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Damping ratio
Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations.
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De Rham curve
In mathematics, a de Rham curve is a certain type of fractal curve named in honor of Georges de Rham.
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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Dianalytic manifold
In mathematics, dianalytic manifolds are possibly non-orientable generalizations of complex analytic manifolds.
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Difference of two squares
In mathematics, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number.
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Diffraction formalism
Diffraction processes affecting waves are amenable to quantitative description and analysis.
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Digital image correlation and tracking
Digital image correlation and tracking is an optical method that employs tracking and image registration techniques for accurate 2D and 3D measurements of changes in images.
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Dihedral group
In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections.
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Dirichlet's unit theorem
In mathematics, Dirichlet's unit theorem is a basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet.
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Discrete Fourier transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.
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Discrete-time Fourier transform
In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to the uniformly-spaced samples of a continuous function.
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Discriminant
In algebra, the discriminant of a polynomial is a polynomial function of its coefficients, which allows deducing some properties of the roots without computing them.
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Division algebra
In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division, except by zero, is always possible.
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Division ring
In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible.
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Dold manifold
In mathematics, a Dold manifold is one of the manifolds P(m,n).
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Dot product
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
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Durand–Kerner method
In numerical analysis, the Durand–Kerner method, discovered by Karl Weierstrass in 1891 and rediscovered independently by Durand in 1960 and Kerner in 1966, is a root-finding algorithm for solving polynomial equations.
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Edmund Schuster
Edmund Schuster (7 September 1851 – 5 July 1932) was a German engineer and mathematician who contributed to the field of special functions and complex analysis being a pioneer in the field of harmonic analysis.
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Eigenfunction
In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Eisenstein integer
In mathematics, Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are complex numbers of the form where and are integers and is a primitive (hence non-real) cube root of unity.
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Eisenstein prime
In mathematics, an Eisenstein prime is an Eisenstein integer that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units, itself and its associates.
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Emmy Noether
Amalie Emmy NoetherEmmy is the Rufname, the second of two official given names, intended for daily use.
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Entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic at all finite points over the whole complex plane.
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Error function
In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion.
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Euler's rotation theorem
In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point.
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Fabry–Pérot interferometer
In optics, a Fabry–Pérot interferometer (FPI) or etalon is typically made of a transparent plate with two reflecting surfaces, or two parallel highly reflecting mirrors.
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Factorization
In mathematics, factorization (also factorisation in some forms of British English) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
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Field of definition
In mathematics, the field of definition of an algebraic variety V is essentially the smallest field to which the coefficients of the polynomials defining V can belong.
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Four-vector
In special relativity, a four-vector (also known as a 4-vector) is an object with four components, which transform in a specific way under Lorentz transformation.
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Fourier transform
The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.
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Fraunhofer diffraction equation
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens.
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Fredholm's theorem
In mathematics, Fredholm's theorems are a set of celebrated results of Ivar Fredholm in the Fredholm theory of integral equations.
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Free particle
In physics, a free particle is a particle that, in some sense, is not bound by an external force, or equivalently not in a region where its potential energy varies.
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Fresnel equations
The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media.
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Frobenius inner product
In mathematics, the Frobenius inner product is a binary operation that takes two matrices and returns a number.
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Fubini–Study metric
In mathematics, the Fubini–Study metric is a Kähler metric on projective Hilbert space, that is, on a complex projective space CPn endowed with a Hermitian form.
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Galois group
In mathematics, more specifically in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.
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Gauss sum
In algebraic number theory, a Gauss sum or Gaussian sum is a particular kind of finite sum of roots of unity, typically where the sum is over elements of some finite commutative ring, is a group homomorphism of the additive group into the unit circle, and is a group homomorphism of the unit group into the unit circle, extended to non-unit where it takes the value 0.
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Gaussian beam
In optics, a Gaussian beam is a beam of monochromatic electromagnetic radiation whose transverse magnetic and electric field amplitude profiles are given by the Gaussian function; this also implies a Gaussian intensity (irradiance) profile.
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Gaussian rational
In mathematics, a Gaussian rational number is a complex number of the form p + qi, where p and q are both rational numbers.
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Generalised circle
A generalized circle, also referred to as a "cline" or "circline", is a straight line or a circle.
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Generalized complex structure
In the field of mathematics known as differential geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and a symplectic structure.
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Generalized dihedral group
In mathematics, the generalized dihedral groups are a family of groups with algebraic structures similar to that of the dihedral groups.
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Generalized Fourier series
In mathematical analysis, many generalizations of Fourier series have proved to be useful.
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Geometry of roots of real polynomials
Graphical methods provide a means of determining or approximating the roots of a polynomial—the values that make the polynomial equal to zero.
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Glossary of field theory
Field theory is the branch of mathematics in which fields are studied.
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Gluon field
In theoretical particle physics, the gluon field is a four vector field characterizing the propagation of gluons in the strong interaction between quarks.
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Group of Lie type
In mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field.
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Hamiltonian (quantum mechanics)
In quantum mechanics, a Hamiltonian is an operator corresponding to the total energy of the system in most of the cases.
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Harmonic wavelet transform
In the mathematics of signal processing, the harmonic wavelet transform, introduced by David Edward Newland in 1993, is a wavelet-based linear transformation of a given function into a time-frequency representation.
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Hölder's inequality
In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of ''Lp'' spaces.
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Hermitian adjoint
In mathematics, specifically in functional analysis, each bounded linear operator on a complex Hilbert space has a corresponding adjoint operator.
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Hermitian function
In mathematical analysis, a Hermitian function is a complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign: (where the ^* indicates the complex conjugate) for all x in the domain of f. This definition extends also to functions of two or more variables, e.g., in the case that f is a function of two variables it is Hermitian if for all pairs (x_1, x_2) in the domain of f. From this definition it follows immediately that: f is a Hermitian function if and only if.
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Hermitian matrix
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the -th row and -th column is equal to the complex conjugate of the element in the -th row and -th column, for all indices and: Hermitian matrices can be understood as the complex extension of real symmetric matrices.
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Hilbert C*-module
Hilbert C*-modules are mathematical objects which generalise the notion of a Hilbert space (which itself is a generalisation of Euclidean space), in that they endow a linear space with an "inner product" which takes values in a C*-algebra.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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History of Lorentz transformations
The history of Lorentz transformations comprises the development of linear transformations forming the Lorentz group or Poincaré group preserving the Lorentz interval -x_0^2+\cdots+x_n^2 and the Minkowski inner product -x_0^2 y_0^2+\cdots+x_n^2 y_n^2.
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Hodge theory
In mathematics, Hodge theory, named after W. V. D. Hodge, uses partial differential equations to study the cohomology groups of a smooth manifold M. The key tool is the Laplacian operator associated to a Riemannian metric on M. The theory was developed by Hodge in the 1930s as an extension of de Rham cohomology.
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Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
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Hopf bifurcation
In the mathematical theory of bifurcations, a Hopf bifurcation is a critical point where a system's stability switches and a periodic solution arises.
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Hopf fibration
In the mathematical field of differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space) in terms of circles and an ordinary sphere.
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Hyperelliptic curve cryptography
Hyperelliptic curve cryptography is similar to elliptic curve cryptography (ECC) insofar as the Jacobian of a hyperelliptic curve is an abelian group in which to do arithmetic, just as we use the group of points on an elliptic curve in ECC.
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Imaginary point
In geometry, in the context of a real geometric space extended to (or embedded in) a complex projective space, an imaginary point is a point not contained in the embedded space.
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Imaginary unit
The imaginary unit or unit imaginary number is a solution to the quadratic equation.
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Impedance bridging
In electronics, especially audio and sound recording, a high impedance bridging, voltage bridging, or simply bridging connection is one in which the load impedance is much larger than the source impedance.
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Impedance matching
In electronics, impedance matching is the practice of designing the input impedance of an electrical load or the output impedance of its corresponding signal source to maximize the power transfer or minimize signal reflection from the load.
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Index of electrical engineering articles
This is an alphabetical list of articles pertaining specifically to electrical and electronics engineering.
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Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
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Input impedance
The input impedance of an electrical network is the measure of the opposition to current flow (impedance), both static (resistance) and dynamic (reactance), into the load network being that is external to the electrical source.
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Invariant (mathematics)
In mathematics, an invariant is a property, held by a class of mathematical objects, which remains unchanged when transformations of a certain type are applied to the objects.
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Inversive geometry
In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion.
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Involution (mathematics)
In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.
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IQ imbalance
IQ imbalance is a performance-limiting issue in the design of direct conversion receivers, also known as zero intermediate frequency (IF) or homodyne receivers.
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ISO 31-11
ISO 31-11:1992 was the part of international standard ISO 31 that defines mathematical signs and symbols for use in physical sciences and technology.
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Isomorphism
In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.
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Isosceles triangle
In geometry, an isosceles triangle is a triangle that has two sides of equal length.
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Jordan normal form
In linear algebra, a Jordan normal form (often called Jordan canonical form) of a linear operator on a finite-dimensional vector space is an upper triangular matrix of a particular form called a Jordan matrix, representing the operator with respect to some basis.
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Joule heating
Joule heating, also known as Ohmic heating and resistive heating, is the process by which the passage of an electric current through a conductor produces heat.
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K-space (magnetic resonance imaging)
k-space is a formalism widely used in magnetic resonance imaging introduced in 1979 by Likes and in 1983 by Ljunggren and Twieg.
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Klein bottle
In topology, a branch of mathematics, the Klein bottle is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined.
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Klein–Gordon equation
The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation.
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Koopman–von Neumann classical mechanics
The Koopman–von Neumann mechanics is a description of classical mechanics in terms of Hilbert space, introduced by Bernard Koopman and John von Neumann in 1931 and 1932.
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Kutta–Joukowski theorem
The Kutta–Joukowski theorem is a fundamental theorem in aerodynamics used for the calculation of lift of an airfoil and any two-dimensional bodies including circular cylinders translating in a uniform fluid at a constant speed large enough so that the flow seen in the body-fixed frame is steady and unseparated.
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Lagrange's identity
In algebra, Lagrange's identity, named after Joseph Louis Lagrange, is: \begin \biggl(\sum_^n a_k^2\biggr) \biggl(\sum_^n b_k^2\biggr) - \biggl(\sum_^n a_k b_k\biggr)^2 &.
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Laplace transform
In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
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LC circuit
An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together.
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Least-squares function approximation
In mathematics, the idea of least squares can be applied to approximating a given function by a weighted sum of other functions.
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Line integral
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve.
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Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
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Linear complex structure
In mathematics, a complex structure on a real vector space V is an automorphism of V that squares to the minus identity, −I.
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Linear difference equation
In mathematics and in particular dynamical systems, a linear difference equation or linear recurrence relation equates 0 to a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence.
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Linear differential equation
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where,..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of an unknown function of the variable.
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Linear map
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
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List of character tables for chemically important 3D point groups
This lists the character tables for the more common molecular point groups used in the study of molecular symmetry.
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List of equations in quantum mechanics
This article summarizes equations in the theory of quantum mechanics.
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List of mathematical symbols
This is a list of symbols used in all branches of mathematics to express a formula or to represent a constant.
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List of mathematical symbols by subject
This list of mathematical symbols by subject shows a selection of the most common symbols that are used in modern mathematical notation within formulas, grouped by mathematical topic.
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Magnitude (mathematics)
In mathematics, magnitude is the size of a mathematical object, a property which determines whether the object is larger or smaller than other objects of the same kind.
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Majorana fermion
A Majorana fermion (uploaded 19 April 2013, retrieved 5 October 2014; and also based on the physicist's name's pronunciation.), also referred to as a Majorana particle, is a fermion that is its own antiparticle.
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Matched filter
In signal processing, a matched filter is obtained by correlating a known signal, or template, with an unknown signal to detect the presence of the template in the unknown signal.
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Mathematical descriptions of opacity
When an electromagnetic wave travels through a medium in which it gets attenuated (this is called an "opaque" or "attenuating" medium), it undergoes exponential decay as described by the Beer–Lambert law.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Matrix consimilarity
In linear algebra, two n-by-n matrices A and B are called consimilar if for some invertible n \times n matrix S, where \bar denotes the elementwise complex conjugation.
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Matrix decomposition
In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices.
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Matrix mechanics
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925.
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Matrix multiplication
In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.
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Matrix representation of Maxwell's equations
In electromagnetism, a branch of fundamental physics, the matrix representations of the Maxwell's equations are a formulation of Maxwell's equations using matrices, complex numbers, and vector calculus.
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Maximum power transfer theorem
In electrical engineering, the maximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals.
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Minimal Supersymmetric Standard Model
The Minimal Supersymmetric Standard Model (MSSM) is an extension to the Standard Model that realizes supersymmetry.
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Minkowski space (number field)
In mathematics, specifically the field of algebraic number theory, a Minkowski space is a Euclidean space associated with an algebraic number field.
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Modulational instability
In the fields of nonlinear optics and fluid dynamics, modulational instability or sideband instability is a phenomenon whereby deviations from a periodic waveform are reinforced by nonlinearity, leading to the generation of spectral-sidebands and the eventual breakup of the waveform into a train of pulses.
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Multiple-scale analysis
In mathematics and physics, multiple-scale analysis (also called the method of multiple scales) comprises techniques used to construct uniformly valid approximations to the solutions of perturbation problems, both for small as well as large values of the independent variables.
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Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.
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Multipliers and centralizers (Banach spaces)
In mathematics, multipliers and centralizers are algebraic objects in the study of Banach spaces.
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Negative resistance
In electronics, negative resistance (NR) is a property of some electrical circuits and devices in which an increase in voltage across the device's terminals results in a decrease in electric current through it.
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Nested radical
In algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression.
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Neutrino oscillation
Neutrino oscillation is a quantum mechanical phenomenon whereby a neutrino created with a specific lepton flavor (electron, muon, or tau) can later be measured to have a different flavor.
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Noether's theorem
Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law.
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Nondimensionalization
Nondimensionalization is the partial or full removal of units from an equation involving physical quantities by a suitable substitution of variables.
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Nonlinear optics
Nonlinear optics (NLO) is the branch of optics that describes the behavior of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light.
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Nonlinear Schrödinger equation
In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation.
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Normal matrix
In mathematics, a complex square matrix is normal if where is the conjugate transpose of.
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Okubo algebra
In algebra, an Okubo algebra or pseudo-octonion algebra is an 8-dimensional non-associative algebra similar to the one studied by.
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Operator (computer programming)
Programming languages typically support a set of operators: constructs which behave generally like functions, but which differ syntactically or semantically from usual functions.
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Orbital overlap
In chemical bonds, an orbital overlap is the concentration of orbitals on adjacent atoms in the same regions of space.
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Orthogonal frequency-division multiplexing
In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies.
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Outer product
In linear algebra, an outer product is the tensor product of two coordinate vectors, a special case of the Kronecker product of matrices.
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Overline
An overline, overscore, or overbar, is a typographical feature of a horizontal line drawn immediately above the text.
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Paraboloid
In geometry, a paraboloid is a quadric surface that has (exactly) one axis of symmetry and no center of symmetry.
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Parseval's theorem
In mathematics, Parseval's theorem usually refers to the result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform.
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Phase correlation
Phase correlation is an approach to estimate the relative translative offset between two similar images (digital image correlation) or other data sets.
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Phase retrieval
Phase retrieval is the process of algorithmically finding solutions to the phase problem.
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Phase-shift keying
Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal (the carrier wave).
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Phasor
In physics and engineering, a phasor (a portmanteau of phase vector), is a complex number representing a sinusoidal function whose amplitude (A), angular frequency (ω), and initial phase (θ) are time-invariant.
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Plane (geometry)
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
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Plane wave expansion
In physics, the plane wave expansion expresses a plane wave as a sum of spherical waves, where.
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Polar decomposition
In mathematics, particularly in linear algebra and functional analysis, the polar decomposition of a matrix or linear operator is a factorization analogous to the polar form of a nonzero complex number z as z.
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Polarization identity
In mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space.
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Pole–zero plot
In mathematics, signal processing and control theory, a pole–zero plot is a graphical representation of a rational transfer function in the complex plane which helps to convey certain properties of the system such as.
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Positive-definite function
In mathematics, a positive-definite function is, depending on the context, either of two types of function.
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Power gain
The power gain of an electrical network is the ratio of an output power to an input power.
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Probability current
In quantum mechanics, the probability current (sometimes called probability flux) is a mathematical quantity describing the flow of probability in terms of probability per unit time per unit area.
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Problem of Apollonius
In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1).
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Progressive function
In mathematics, a progressive function ƒ ∈ L2(R) is a function whose Fourier transform is supported by positive frequencies only: It is called super regressive if and only if the time reversed function f(−t) is progressive, or equivalently, if The complex conjugate of a progressive function is regressive, and vice versa.
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Proofs involving the Moore–Penrose inverse
In linear algebra, the Moore-Penrose inverse is a matrix that satisfies some but not necessarily all of the properties of an inverse matrix.
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Pulse compression
Pulse compression is a signal processing technique commonly used by radar, sonar and echography to increase the range resolution as well as the signal to noise ratio.
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Q factor
In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is, and characterizes a resonator's bandwidth relative to its centre frequency.
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Quadratic equation
In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.
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Quadratic formula
In elementary algebra, the quadratic formula is the solution of the quadratic equation.
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Quadric
In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).
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Quantization of the electromagnetic field
The quantization of the electromagnetic field, means that an electromagnetic field consists of discrete energy parcels, photons.
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Quantum state
In quantum physics, quantum state refers to the state of an isolated quantum system.
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Quartic function
In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.
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Quartic reciprocity
Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence x4 ≡ p (mod q) to that of x4 ≡ q (mod p).
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Quaternionic analysis
In mathematics, quaternionic analysis is the study of functions with quaternions as the domain and/or range.
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Rabi problem
The Rabi problem concerns the response of an atom to an applied harmonic electric field, with an applied frequency very close to the atom's natural frequency.
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Rayleigh's equation (fluid dynamics)
In fluid dynamics, Rayleigh's equation or Rayleigh stability equation is a linear ordinary differential equation to study the hydrodynamic stability of a parallel, incompressible and inviscid shear flow.
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Real coordinate space
In mathematics, real coordinate space of dimensions, written R (also written with blackboard bold) is a coordinate space that allows several (''n'') real variables to be treated as a single variable.
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Real representation
In the mathematical field of representation theory a real representation is usually a representation on a real vector space U, but it can also mean a representation on a complex vector space V with an invariant real structure, i.e., an antilinear equivariant map which satisfies The two viewpoints are equivalent because if U is a real vector space acted on by a group G (say), then V.
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Real structure
In mathematics, a real structure on a complex vector space is a way to decompose the complex vector space in the direct sum of two real vector spaces.
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Reality structure
In mathematics, a reality structure on a complex vector space V is a decomposition of V into two real subspaces, called the real and imaginary parts of V: Here VR is a real subspace of V, i.e. a subspace of V considered as a vector space over the real numbers.
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Reciprocal polynomial
In algebra, the reciprocal polynomial, or reflected polynomial* or, of a polynomial of degree with coefficients from an arbitrary field, such as is the polynomial Essentially, the coefficients are written in reverse order.
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Reciprocity (electromagnetism)
In classical electromagnetism, reciprocity refers to a variety of related theorems involving the interchange of time-harmonic electric current densities (sources) and the resulting electromagnetic fields in Maxwell's equations for time-invariant linear media under certain constraints.
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Refinable function
In mathematics, in the area of wavelet analysis, a refinable function is a function which fulfils some kind of self-similarity.
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Representation theory of the Lorentz group
The Lorentz group is a Lie group of symmetries of the spacetime of special relativity.
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Ricci scalars (Newman–Penrose formalism)
In the Newman–Penrose (NP) formalism of general relativity, independent components of the Ricci tensors of a four-dimensional spacetime are encoded into seven (or ten) Ricci scalars which consist of three real scalars \, three (or six) complex scalars \ and the NP curvature scalar \Lambda.
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Riemann surface
In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.
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Ring homomorphism
In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the structure.
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Root of unity
In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that gives 1 when raised to some positive integer power.
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Rotating wave approximation
The rotating wave approximation is an approximation used in atom optics and magnetic resonance.
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Rotation matrix
In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space.
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Sato–Tate conjecture
In mathematics, the Sato–Tate conjecture is a statistical statement about the family of elliptic curves Ep over the finite field with p elements, with p a prime number, obtained from an elliptic curve E over the rational number field, by the process of reduction modulo a prime for almost all p. If Np denotes the number of points on Ep and defined over the field with p elements, the conjecture gives an answer to the distribution of the second-order term for Np.
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Scattering parameters
Scattering parameters or S-parameters (the elements of a scattering matrix or S-matrix) describe the electrical behavior of linear electrical networks when undergoing various steady state stimuli by electrical signals.
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Schrödinger equation
In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are significant.
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Schwarzschild geodesics
In general relativity, Schwarzschild geodesics describe the motion of particles of infinitesimal mass in the gravitational field of a central fixed mass M. Schwarzschild geodesics have been pivotal in the validation of Einstein's theory of general relativity.
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Schwinger function
In quantum field theory, the Wightman distributions can be analytically continued to analytic functions in Euclidean space with the domain restricted to the ordered set of points in Euclidean space with no coinciding points.
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Seesaw mechanism
In the theory of grand unification of particle physics, and, in particular, in theories of neutrino masses and neutrino oscillation, the seesaw mechanism is a generic model used to understand the relative sizes of observed neutrino masses, of the order of eV, compared to those of quarks and charged leptons, which are millions of times heavier.
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Sesquilinear form
In mathematics, a sesquilinear form is a generalization of a bilinear form that, in turn, is a generalization of the concept of the dot product of Euclidean space.
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Simson line
In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear.
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Singular point of an algebraic variety
In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric sense that at this point the tangent space at the variety may not be regularly defined.
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Skew-Hermitian matrix
In linear algebra, a square matrix with complex entries is said to be skew-Hermitian or antihermitian if its conjugate transpose is equal to the original matrix, with all the entries being of opposite sign.
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SL2(R)
In mathematics, the special linear group SL(2,R) or SL2(R) is the group of 2 × 2 real matrices with determinant one: a & b \\ c & d \end \right): a,b,c,d\in\mathbf\mboxad-bc.
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Slater-type orbital
Slater-type orbitals (STOs) are functions used as atomic orbitals in the linear combination of atomic orbitals molecular orbital method.
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Space–time block code
Space–time block coding is a technique used in wireless communications to transmit multiple copies of a data stream across a number of antennas and to exploit the various received versions of the data to improve the reliability of data transfer.
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Special unitary group
In mathematics, the special unitary group of degree, denoted, is the Lie group of unitary matrices with determinant 1.
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Spectral density
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal.
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Spectral theory
In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces.
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Spherical basis
In pure and applied mathematics, particularly quantum mechanics and computer graphics and their applications, a spherical basis is the basis used to express spherical tensors.
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Spinor
In geometry and physics, spinors are elements of a (complex) vector space that can be associated with Euclidean space.
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Split-quaternion
In abstract algebra, the split-quaternions or coquaternions are elements of a 4-dimensional associative algebra introduced by James Cockle in 1849 under the latter name.
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Square matrix
In mathematics, a square matrix is a matrix with the same number of rows and columns.
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Square-integrable function
In mathematics, a square-integrable function, also called a quadratically integrable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite.
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Staggered tuning
Staggered tuning is a technique used in the design of multi-stage tuned amplifiers whereby each stage is tuned to a slightly different frequency.
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Standing wave ratio
In radio engineering and telecommunications, standing wave ratio (SWR) is a measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide.
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Stationary phase approximation
In mathematics, the stationary phase approximation is a basic principle of asymptotic analysis, applying to oscillatory integrals taken over n-dimensional space ℝn where i is the imaginary unit.
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Stokes' paradox
In the science of fluid flow, Stokes' paradox is the phenomenon that there can be no creeping flow of a fluid around a disk in two dimensions; or, equivalently, the fact there is no non-trivial steady-state solution for the Stokes equations around an infinitely long cylinder.
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Stone–Weierstrass theorem
In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval can be uniformly approximated as closely as desired by a polynomial function.
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Symmetry in mathematics
Symmetry occurs not only in geometry, but also in other branches of mathematics.
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Symmetry in quantum mechanics
Symmetries in quantum mechanics describe features of spacetime and particles which are unchanged under some transformation, in the context of quantum mechanics, relativistic quantum mechanics and quantum field theory, and with applications in the mathematical formulation of the standard model and condensed matter physics.
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T-symmetry
T-symmetry or time reversal symmetry is the theoretical symmetry of physical laws under the transformation of time reversal: T-symmetry can be shown to be equivalent to the conservation of entropy, by Noether's Theorem.
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Tensor rank decomposition
In multilinear algebra, the tensor rank decomposition or canonical polyadic decomposition (CPD) may be regarded as a generalization of the matrix singular value decomposition (SVD) to tensors, which has found application in statistics, signal processing, psychometrics, linguistics and chemometrics.
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Transpose
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal, that is it switches the row and column indices of the matrix by producing another matrix denoted as AT (also written A′, Atr, tA or At).
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Two-dimensional conformal field theory
A two-dimensional conformal field theory is a quantum field theory on a Euclidean two-dimensional space, that is invariant under local conformal transformations.
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Uncertainty principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.
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Unitary group
In mathematics, the unitary group of degree n, denoted U(n), is the group of unitary matrices, with the group operation of matrix multiplication.
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Unitary transformation
In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation.
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Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.
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Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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Vector spherical harmonics
In mathematics, vector spherical harmonics (VSH) are an extension of the scalar spherical harmonics for use with vector fields.
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Wave function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system.
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Wave function collapse
In quantum mechanics, wave function collapse is said to occur when a wave function—initially in a superposition of several eigenstates—appears to reduce to a single eigenstate (by "observation").
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Wave interference
In physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude.
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Wavelet transform modulus maxima method
The wavelet transform modulus maxima (WTMM) is a method for detecting the fractal dimension of a signal.
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Wiener deconvolution
In mathematics, Wiener deconvolution is an application of the Wiener filter to the noise problems inherent in deconvolution.
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Wirtinger derivatives
In complex analysis of one and several complex variables, Wirtinger derivatives (sometimes also called Wirtinger operators), named after Wilhelm Wirtinger who introduced them in 1927 in the course of his studies on the theory of functions of several complex variables, are partial differential operators of the first order which behave in a very similar manner to the ordinary derivatives with respect to one real variable, when applied to holomorphic functions, antiholomorphic functions or simply differentiable functions on complex domains.
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X-ray crystallography
X-ray crystallography is a technique used for determining the atomic and molecular structure of a crystal, in which the crystalline atoms cause a beam of incident X-rays to diffract into many specific directions.
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XPIC
XPIC, or cross-polarization interference cancelling technology, is an algorithm to suppress mutual interference between two received streams in a Polarization-division multiplexing communication system.
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Z N model
The Z_N model is a simplified statistical mechanical spin model.
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Z-transform
In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency domain representation.
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Zero of a function
In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).
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Redirects here:
Complex Conjugate, Complex conjugacy, Complex conjugation, Conjugate complex.
References
[1] https://en.wikipedia.org/wiki/Complex_conjugate
