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Orthogonality

Index Orthogonality

In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms. [1]

125 relations: A Greek–English Lexicon, Addressing mode, Adriaan van Wijngaarden, ALGOL 68, Analytical chemistry, Ancient Greek, Asymmetric digital subscriber line, Basis (linear algebra), Basis function, Bilinear form, Bioorthogonal chemistry, Bra–ket notation, Burgoyne Diller, Chebyshev polynomials, Chess, Combinatorics, Confluence (abstract rewriting), Correlation and dependence, Dependent and independent variables, DNA, Dot product, Dual pair, DVB-T, Econometrics, Eigenvalues and eigenvectors, Euclidean space, Euclidean vector, Expected value, Exponential distribution, Fourier series, Function (mathematics), Function space, Functional group, G.hn, Gamma distribution, Generalized method of moments, Geometry, Go (game), Gram–Schmidt process, Greg Egan, Hermite polynomials, Hyperbolic orthogonality, Hyperplane, IEEE 802.11, If and only if, Imaginary number, Inner product space, Instruction set architecture, Integral, Isogonal, ..., ITU-T, Kronecker delta, Laguerre polynomials, Latin square, Legendre polynomials, Line (geometry), Linear algebra, Linear subspace, Mathematician, Mathematics, Maximum likelihood estimation, Module (mathematics), Motorola 68000, Neuroscience, New Drug Application, Non-covalent interactions, Norm (mathematics), Normal (geometry), Normal distribution, Ordinary least squares, Organic synthesis, Orthogonal complement, Orthogonal frequency-division multiplexing, Orthogonal functions, Orthogonal group, Orthogonal instruction set, Orthogonal ligand-protein pair, Orthogonal matrix, Orthogonal polynomials, Orthogonal trajectory, Orthogonality (term rewriting), Orthogonalization, Orthonormal basis, Orthonormality, Oxford English Dictionary, Perpendicular, Perspective (graphical), Piet Mondrian, Plane (geometry), Probability, Processor register, Protecting group, Pseudo-Euclidean space, Quantum mechanics, Radian, Rectangle, Regression analysis, Rewriting, Riemann integral, Right angle, Right triangle, Schrödinger equation, Self-adjoint operator, Separation of concerns, Simple linear regression, Split-quaternion, Statistics, Sturm–Liouville theory, Subcarrier, Superimposition, Supramolecular chemistry, Taxonomy (general), The Art of Unix Programming, The Road to Reality, Thyssen-Bornemisza Museum, Time-division multiple access, Uniform distribution (continuous), Unit vector, Vanishing point, Vector space, Website, Weight function, Wi-Fi, Wigner semicircle distribution, WiMAX. Expand index (75 more) »

A Greek–English Lexicon

A Greek–English Lexicon, often referred to as Liddell & Scott, Liddell–Scott–Jones, or LSJ, is a standard lexicographical work of the Ancient Greek language.

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Addressing mode

Addressing modes are an aspect of the instruction set architecture in most central processing unit (CPU) designs.

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Adriaan van Wijngaarden

Adriaan "Aad" van Wijngaarden (2 November 1916 – 7 February 1987) was a Dutch mathematician and computer scientist, who is considered by many to have been the founding father of informatica (computer science) in the Netherlands.

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ALGOL 68

ALGOL 68 (short for Algorithmic Language 1968) is an imperative computer programming language that was conceived as a successor to the ALGOL 60 programming language, designed with the goal of a much wider scope of application and more rigorously defined syntax and semantics.

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Analytical chemistry

Analytical chemistry studies and uses instruments and methods used to separate, identify, and quantify matter.

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Ancient Greek

The Ancient Greek language includes the forms of Greek used in ancient Greece and the ancient world from around the 9th century BC to the 6th century AD.

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Asymmetric digital subscriber line

Asymmetric digital subscriber line (ADSL) is a type of digital subscriber line (DSL) technology, a data communications technology that enables faster data transmission over copper telephone lines than a conventional voiceband modem can provide.

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Basis (linear algebra)

In mathematics, a set of elements (vectors) in a vector space V is called a basis, or a set of, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.

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Basis function

In mathematics, a basis function is an element of a particular basis for a function space.

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Bilinear form

In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map, where K is the field of scalars.

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Bioorthogonal chemistry

The term bioorthogonal chemistry refers to any chemical reaction that can occur inside of living systems without interfering with native biochemical processes.

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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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Burgoyne Diller

Burgoyne A. Diller (January 13, 1906 – January 30, 1965) was an American abstract painter.

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Chebyshev polynomials

In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively.

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Chess

Chess is a two-player strategy board game played on a chessboard, a checkered gameboard with 64 squares arranged in an 8×8 grid.

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Combinatorics

Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.

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Confluence (abstract rewriting)

In computer science, confluence is a property of rewriting systems, describing which terms in such a system can be rewritten in more than one way, to yield the same result.

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Correlation and dependence

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data.

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Dependent and independent variables

In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.

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DNA

Deoxyribonucleic acid (DNA) is a thread-like chain of nucleotides carrying the genetic instructions used in the growth, development, functioning and reproduction of all known living organisms and many viruses.

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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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Dual pair

In functional analysis and related areas of mathematics a dual pair or dual system is a pair of vector spaces with an associated bilinear map to the base field.

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DVB-T

DVB-T is an abbreviation for "Digital Video Broadcasting — Terrestrial"; it is the DVB European-based consortium standard for the broadcast transmission of digital terrestrial television that was first published in 1997 and first broadcast in the UK in 1998.

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Econometrics

Econometrics is the application of statistical methods to economic data and is described as the branch of economics that aims to give empirical content to economic relations.

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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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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

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Expected value

In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.

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Exponential distribution

No description.

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Fourier series

In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Function space

In mathematics, a function space is a set of functions between two fixed sets.

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Functional group

In organic chemistry, functional groups are specific substituents or moieties within molecules that are responsible for the characteristic chemical reactions of those molecules.

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G.hn

G.hn is a specification for home networking with data rates up to 2 Gbit/s and operation over four types of legacy wires: telephone wiring, coaxial cables, power lines and plastic optical fiber.

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Gamma distribution

In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions.

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Generalized method of moments

In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models.

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Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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Go (game)

Go is an abstract strategy board game for two players, in which the aim is to surround more territory than the opponent.

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Gram–Schmidt process

In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process is a method for orthonormalising a set of vectors in an inner product space, most commonly the Euclidean space Rn equipped with the standard inner product.

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Greg Egan

Greg Egan (born 20 August 1961) is an Australian science fiction writer.

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Hermite polynomials

In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence.

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Hyperbolic orthogonality

In plane geometry, two lines are hyperbolic orthogonal when they are reflections of each other over the asymptote of a given hyperbola.

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Hyperplane

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space.

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IEEE 802.11

IEEE 802.11 is a set of media access control (MAC) and physical layer (PHY) specifications for implementing wireless local area network (WLAN) computer communication in the 900 MHz and 2.4, 3.6, 5, and 60 GHz frequency bands.

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If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

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Imaginary number

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit,j is usually used in Engineering contexts where i has other meanings (such as electrical current) which is defined by its property.

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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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Instruction set architecture

An instruction set architecture (ISA) is an abstract model of a computer.

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Integral

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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Isogonal

Isogonal is a mathematical term which means "having similar angles".

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ITU-T

The ITU Telecommunication Standardization Sector (ITU-T) is one of the three sectors (divisions or units) of the International Telecommunication Union (ITU); it coordinates standards for telecommunications.

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Kronecker delta

In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.

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Laguerre polynomials

In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 - 1886), are solutions of Laguerre's equation: which is a second-order linear differential equation.

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Latin square

In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column.

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Legendre polynomials

In mathematics, Legendre functions are solutions to Legendre's differential equation: They are named after Adrien-Marie Legendre.

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Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

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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 subspace

In linear algebra and related fields of mathematics, a linear subspace, also known as a vector subspace, or, in the older literature, a linear manifold, is a vector space that is a subset of some other (higher-dimension) vector space.

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Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model, given observations.

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Module (mathematics)

In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.

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Motorola 68000

The Motorola 68000 ("'sixty-eight-thousand'"; also called the m68k or Motorola 68k, "sixty-eight-kay") is a 16/32-bit CISC microprocessor, which implements a 32-bit instruction set, with 32-bit registers and 32-bit internal data bus, but with a 16-bit data ALU and two 16-bit arithmetic ALUs and a 16-bit external data bus, designed and marketed by Motorola Semiconductor Products Sector.

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Neuroscience

Neuroscience (or neurobiology) is the scientific study of the nervous system.

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New Drug Application

The Food and Drug Administration's New Drug Application (NDA) is the vehicle in the United States through which drug sponsors formally propose that the FDA approve a new pharmaceutical for sale and marketing.

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Non-covalent interactions

A non-covalent interaction differs from a covalent bond in that it does not involve the sharing of electrons, but rather involves more dispersed variations of electromagnetic interactions between molecules or within a molecule.

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Norm (mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.

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Normal (geometry)

In geometry, a normal is an object such as a line or vector that is perpendicular to a given object.

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Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.

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Ordinary least squares

In statistics, ordinary least squares (OLS) or linear least squares is a method for estimating the unknown parameters in a linear regression model.

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Organic synthesis

Organic synthesis is a special branch of chemical synthesis and is concerned with the intentional construction of organic compounds.

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Orthogonal complement

In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace W of a vector space V equipped with a bilinear form B is the set W⊥ of all vectors in V that are orthogonal to every vector in W. Informally, it is called the perp, short for perpendicular complement.

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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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Orthogonal functions

In mathematics, orthogonal functions belong to a function space which is a vector space that has a bilinear form.

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Orthogonal group

In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.

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Orthogonal instruction set

In computer engineering, an orthogonal instruction set is an instruction set architecture where all instruction types can use all addressing modes.

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Orthogonal ligand-protein pair

Orthogonal ligand-protein pairs (also known as re-engineered ligand-receptor interfaces or re-engineered enzyme-substrate interactions) are a protein-ligand binding pair made to be independent of the original binding pair.

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Orthogonal matrix

In linear algebra, an orthogonal matrix is a square matrix whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors), i.e. where I is the identity matrix.

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Orthogonal polynomials

In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product.

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Orthogonal trajectory

In mathematics an orthogonal trajectory is.

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Orthogonality (term rewriting)

Orthogonality as a property of term rewriting systems describes where the reduction rules of the system are all left-linear, that is each variable occurs only once on the left hand side of each reduction rule, and there is no overlap between them.

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Orthogonalization

In linear algebra, orthogonalization is the process of finding a set of orthogonal vectors that span a particular subspace.

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Orthonormal basis

In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other.

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Orthonormality

In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and unit vectors.

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Oxford English Dictionary

The Oxford English Dictionary (OED) is the main historical dictionary of the English language, published by the Oxford University Press.

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Perpendicular

In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).

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Perspective (graphical)

Perspective (from perspicere "to see through") in the graphic arts is an approximate representation, generally on a flat surface (such as paper), of an image as it is seen by the eye.

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Piet Mondrian

Pieter Cornelis "Piet" Mondriaan, after 1906 Mondrian (later; 7 March 1872 – 1 February 1944), was a Dutch painter and theoretician who is regarded as one of the greatest artists of the 20th century.

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Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

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Probability

Probability is the measure of the likelihood that an event will occur.

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Processor register

In computer architecture, a processor register is a quickly accessible location available to a computer's central processing unit (CPU).

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Protecting group

A protecting group or protective group is introduced into a molecule by chemical modification of a functional group to obtain chemoselectivity in a subsequent chemical reaction.

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Pseudo-Euclidean space

In mathematics and theoretical physics, a pseudo-Euclidean space is a finite-dimensional ''n''-space together with a non-degenerate quadratic form.

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Quantum mechanics

Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

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Radian

The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.

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Rectangle

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.

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Regression analysis

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships among variables.

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Rewriting

In mathematics, computer science, and logic, rewriting covers a wide range of (potentially non-deterministic) methods of replacing subterms of a formula with other terms.

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Riemann integral

In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval.

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Right angle

In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn.

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Right triangle

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle).

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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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Self-adjoint operator

In mathematics, a self-adjoint operator on a finite-dimensional complex vector space V with inner product \langle\cdot,\cdot\rangle is a linear map A (from V to itself) that is its own adjoint: \langle Av,w\rangle.

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Separation of concerns

In computer science, separation of concerns (SoC) is a design principle for separating a computer program into distinct sections, such that each section addresses a separate concern.

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Simple linear regression

In statistics, simple linear regression is a linear regression model with a single explanatory variable.

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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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Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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Sturm–Liouville theory

In mathematics and its applications, a classical Sturm–Liouville theory, named after Jacques Charles François Sturm (1803–1855) and Joseph Liouville (1809–1882), is the theory of a real second-order linear differential equation of the form where y is a function of the free variable x. Here the functions p(x), q(x), and w(x) > 0 are specified at the outset.

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Subcarrier

A subcarrier is a sideband of a radio frequency carrier wave, which is modulated to send additional information.

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Superimposition

Superimposition is the placement of one thing over another, typically so that both are still evident.

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Supramolecular chemistry

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Taxonomy (general)

Taxonomy is the practice and science of classification.

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The Art of Unix Programming

The Art of Unix Programming by Eric S. Raymond is a book about the history and culture of Unix programming from its earliest days in 1969 to 2003 when it was published, covering both genetic derivations such as BSD and conceptual ones such as Linux.

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The Road to Reality

The Road to Reality: A Complete Guide to the Laws of the Universe is a book on modern physics by the British mathematical physicist Roger Penrose, published in 2004.

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Thyssen-Bornemisza Museum

The Thyssen-Bornemisza Museum (in Spanish, the Museo Thyssen-Bornemisza, named after its founder), or simply the Thyssen, is an art museum in Madrid, Spain, located near the Prado Museum on one of city's main boulevards.

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Time-division multiple access

Time-division multiple access (TDMA) is a channel access method for shared-medium networks.

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Uniform distribution (continuous)

In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.

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Unit vector

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

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Vanishing point

A vanishing point is a point on the image plane of a perspective drawing where the two-dimensional perspective projections (or drawings) of mutually parallel lines in three-dimensional space appear to converge.

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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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Website

A website is a collection of related web pages, including multimedia content, typically identified with a common domain name, and published on at least one web server.

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Weight function

A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set.

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Wi-Fi

Wi-Fi or WiFi is technology for radio wireless local area networking of devices based on the IEEE 802.11 standards.

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Wigner semicircle distribution

The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution supported on the interval the graph of whose probability density function f is a semicircle of radius R centered at (0, 0) and then suitably normalized (so that it is really a semi-ellipse): for −R ≤ x ≤ R, and f(x).

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WiMAX

WiMAX (Worldwide Interoperability for Microwave Access) is a family of wireless communication standards based on the IEEE 802.16 set of standards, which provide multiple physical layer (PHY) and Media Access Control (MAC) options.

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References

[1] https://en.wikipedia.org/wiki/Orthogonality

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