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222 relations: A History of Vector Analysis, A Treatise on Electricity and Magnetism, Abelian group, Abstract algebra, Alexander Macfarlane, Algebra, American Mathematical Society, Andrew Wiles, Applied mathematics, Artin–Wedderburn theorem, Associative algebra, Associative property, Attitude control, Banach algebra, Basis (linear algebra), Binary icosahedral group, Bioinformatics, Biquaternion, Bivector, Blackboard bold, Brauer group, Broom Bridge, Carl Friedrich Gauss, Cayley–Dickson construction, Center (ring theory), Central simple algebra, Charles Jasper Joly, Chris J. L. Doran, Classical electromagnetism, Classical Hamiltonian quaternions, Classification of Clifford algebras, Clifford algebra, Combinatorial design, Commutative property, Complex analysis, Complex number, Composition algebra, Computer graphics, Computer simulation, Computer vision, Conformal geometry, Conformal map, Conjugacy class, Conjugate element (field theory), Conjugate transpose, Control theory, Conversion between quaternions and Euler angles, Covering space, Cross product, Crystallography, ..., Defence Research and Development Canada, Determinant, Differential equation, Dimension (vector space), Distributive property, Division algebra, Division ring, Domain (ring theory), Dot product, Dual quaternion, Dublin, Dunsink Observatory, Encyclopædia Britannica, Euclidean algorithm, Euclidean vector, Euler angles, Euler's four-square identity, Euler–Rodrigues formula, Exponentiation, Expression (mathematics), Exterior algebra, Field (mathematics), Field extension, Four-dimensional space, Frobenius theorem (real division algebras), Geometric algebra, Geometry, Gimbal lock, Group (mathematics), Group isomorphism, Group representation, Group ring, Hermann von Helmholtz, Homogeneous coordinates, Homomorphism, Hurwitz quaternion, Hurwitz quaternion order, Hurwitz's theorem (composition algebras), Hyperbolic quaternion, Hypercomplex number, Ian R. Porteous, Icosahedral symmetry, Icosian, Ideal (ring theory), Identity element, Imaginary unit, Injective function, Integer, Involution (mathematics), James Clerk Maxwell, Joachim Lambek, John C. Baez, John Horton Conway, Josiah Willard Gibbs, Julia set, Kinematics, Laplace–Runge–Lenz vector, Lattice (group), Lénárt sphere, Lie group, List of mathematical symbols, Longman, Lorentz group, Ludwik Silberstein, Mathematics, Matrix (mathematics), Matrix multiplication, Matrix ring, Maxwell's equations, Maynooth University, Mechanics, Metric space, Michiel Hazewinkel, Molecular dynamics, Morgan Kaufmann Publishers, Multiplication table, Multiplicative inverse, Murray Gell-Mann, National Council of Teachers of Mathematics, Non-associative algebra, Noncommutative ring, Norm (mathematics), Number, Number theory, Octahedron, Octonion, Olinde Rodrigues, Oliver Heaviside, Orbital mechanics, Orthogonal matrix, Patrick du Val, Pauli matrices, Peter Tait (physicist), Physics, Plane (geometry), Plate trick, Point (geometry), Point groups in three dimensions, Polar decomposition, Polynomial, PostScript, Potential, Princeton University Press, Pseudovector, Pure mathematics, Quadratic form, Quantum mechanics, Quaternion group, Quaternion Society, Quaternionic analysis, Quaternionic matrix, Quaternionic projective space, Quaternions and spatial rotation, Quotient, Quotient ring, Rational number, Real line, Real number, Regular icosahedron, Rigid body, Ring (mathematics), Robotics, Rotation (mathematics), Rotation group SO(3), Rotation matrix, Rotations in 4-dimensional Euclidean space, Rotor (mathematics), Royal Canal, Royal Irish Academy, Schläfli symbol, Sedenion, SIGGRAPH, Signal processing, Simple algebra, Slerp, Space, Space group, Spacetime, Special unitary group, Sphere, Spin (physics), Spin group, Split-biquaternion, Split-quaternion, Steven Weinberg, Subring, Tensor, Tesseract, Tetrahedron, Texture (crystalline), Thomas precession, Three-dimensional space, Tomb Raider, Transpose, Truncated 24-cells, Unicode, Unit sphere, Unitary matrix, University of Dublin, Vector calculus, Vector space, Versor, Wilhelm Blaschke, William Edwin Hamilton, William Rowan Hamilton, William Thomson, 1st Baron Kelvin, Zero divisor, 2 × 2 real matrices, 24-cell, 3-sphere, 3D computer graphics, 600-cell. Expand index (172 more) »
A History of Vector Analysis
A History of Vector Analysis (1967) is a book on the history of vector analysis by Michael J. Crowe, originally published by the University of Notre Dame Press.
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A Treatise on Electricity and Magnetism
A Treatise on Electricity and Magnetism is a two-volume treatise on electromagnetism written by James Clerk Maxwell in 1873.
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Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
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Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
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Alexander Macfarlane
Prof Alexander Macfarlane FRSE LLD (21 April 1851 – 28 August 1913) was a Scottish logician, physicist, and mathematician.
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Algebra
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
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American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Andrew Wiles
Sir Andrew John Wiles (born 11 April 1953) is a British mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory.
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Applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry.
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Artin–Wedderburn theorem
In algebra, the Artin–Wedderburn theorem is a classification theorem for semisimple rings and semisimple algebras.
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Associative algebra
In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.
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Associative property
In mathematics, the associative property is a property of some binary operations.
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Attitude control
Attitude control is controlling the orientation of an object with respect to an inertial frame of reference or another entity like the celestial sphere, certain fields, and nearby objects, etc.
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Banach algebra
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, i.e. a normed space and complete in the metric induced by the norm.
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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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Binary icosahedral group
In mathematics, the binary icosahedral group 2I or is a certain nonabelian group of order 120.
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Bioinformatics
Bioinformatics is an interdisciplinary field that develops methods and software tools for understanding biological data.
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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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Bivector
In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors.
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Blackboard bold
Blackboard bold is a typeface style that is often used for certain symbols in mathematical texts, in which certain lines of the symbol (usually vertical or near-vertical lines) are doubled.
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Brauer group
In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras.
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Broom Bridge
Broom Bridge (Irish: Droichead Broome), also called Broome Bridge, and sometimes Brougham Bridge, is a bridge along Broombridge Road which crosses the Royal Canal in Cabra, Dublin, Ireland.
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Carl Friedrich Gauss
Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.
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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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Center (ring theory)
In algebra, the center of a ring R is the subring consisting of the elements x such that xy.
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Central simple algebra
In ring theory and related areas of mathematics a central simple algebra (CSA) over a field K is a finite-dimensional associative algebra A, which is simple, and for which the center is exactly K. In other words, any simple algebra is a central simple algebra over its center.
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Charles Jasper Joly
Charles Jasper Joly (27 June 1864 – 4 January 1906) was an Irish mathematician and astronomer who became Royal Astronomer of Ireland.
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Chris J. L. Doran
Chris J. L. Doran is a physicist, Director of Studies in Natural Sciences for Sidney Sussex College, Cambridge.
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Classical electromagnetism
Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model.
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Classical Hamiltonian quaternions
William Rowan Hamilton invented quaternions, a mathematical entity in 1843.
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Classification of Clifford algebras
In abstract algebra, in particular in the theory of nondegenerate quadratic forms on vector spaces, the structures of finite-dimensional real and complex Clifford algebras for a nondegenerate quadratic form have been completely classified.
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Clifford algebra
In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra.
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Combinatorial design
Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry.
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Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
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Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
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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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Composition algebra
In mathematics, a composition algebra over a field is a not necessarily associative algebra over together with a nondegenerate quadratic form that satisfies for all and in.
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Computer graphics
Computer graphics are pictures and films created using computers.
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Computer simulation
Computer simulation is the reproduction of the behavior of a system using a computer to simulate the outcomes of a mathematical model associated with said system.
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Computer vision
Computer vision is a field that deals with how computers can be made for gaining high-level understanding from digital images or videos.
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Conformal geometry
In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space.
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Conformal map
In mathematics, a conformal map is a function that preserves angles locally.
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Conjugacy class
In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.
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Conjugate element (field theory)
In mathematics, in particular field theory, the conjugate elements of an algebraic element α, over a field extension L/K, are the roots of the minimal polynomial pK,α(x) of α over K. Conjugate elements are also called Galois conjugates or simply conjugates.
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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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Control theory
Control theory in control systems engineering deals with the control of continuously operating dynamical systems in engineered processes and machines.
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Conversion between quaternions and Euler angles
Spatial rotations in three dimensions can be parametrized using both Euler angles and unit quaternions.
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Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.
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Cross product
In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space \left(\mathbb^3\right) and is denoted by the symbol \times.
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Crystallography
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure).
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Defence Research and Development Canada
Defence Research and Development Canada (DRDC; Recherche et développement pour la défense Canada, RDDC) in French), is an agency of the Department of National Defence (DND), whose purpose is to provide the Canadian Armed Forces (CAF), other government departments, and public safety and national security communities with knowledge and technology. DRDC has approximately 1,400 employees across eight research centres within Canada.
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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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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Dimension (vector space)
In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.
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Distributive property
In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.
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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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Domain (ring theory)
In mathematics, and more specifically in algebra, a domain is a nonzero ring in which implies or.
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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 quaternion
In mathematics and mechanics, the set of dual quaternions is a Clifford algebra that can be used to represent spatial rigid body displacements.
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Dublin
Dublin is the capital of and largest city in Ireland.
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Dunsink Observatory
The Dunsink Observatory is an astronomical observatory established in 1785 in the townland of Dunsink near the city of Dublin, Ireland.
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Encyclopædia Britannica
The Encyclopædia Britannica (Latin for "British Encyclopaedia"), published by Encyclopædia Britannica, Inc., is a general knowledge English-language encyclopaedia.
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Euclidean algorithm
. EXAMPLES CAN BE FOUND BELOW, E.G., IN THE "Matrix method" SECTION.
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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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Euler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system.
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Euler's four-square identity
In mathematics, Euler's four-square identity says that the product of two numbers, each of which is a sum of four squares, is itself a sum of four squares.
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Euler–Rodrigues formula
In mathematics and mechanics, the Euler–Rodrigues formula describes the rotation of a vector in three dimensions.
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Exponentiation
Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.
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Expression (mathematics)
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
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Exterior algebra
In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.
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Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
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Field extension
In mathematics, and in particular, algebra, a field E is an extension field of a field F if E contains F and the operations of F are those of E restricted to F. Equivalently, F is a subfield of E. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers.
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Four-dimensional space
A four-dimensional space or 4D space is a mathematical extension of the concept of three-dimensional or 3D space.
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Frobenius theorem (real division algebras)
In mathematics, more specifically in abstract algebra, the Frobenius theorem, proved by Ferdinand Georg Frobenius in 1877, characterizes the finite-dimensional associative division algebras over the real numbers.
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Geometric algebra
The geometric algebra (GA) of a vector space is an algebra over a field, noted for its multiplication operation called the geometric product on a space of elements called multivectors, which is a superset of both the scalars F and the vector space V. Mathematically, a geometric algebra may be defined as the Clifford algebra of a vector space with a quadratic form.
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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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Gimbal lock
Gimbal lock is the loss of one degree of freedom in a three-dimensional, three-gimbal mechanism that occurs when the axes of two of the three gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate two-dimensional space.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Group isomorphism
In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations.
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Group representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication.
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Group ring
In algebra, a group ring is a free module and at the same time a ring, constructed in a natural way from any given ring and any given group.
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Hermann von Helmholtz
Hermann Ludwig Ferdinand von Helmholtz (August 31, 1821 – September 8, 1894) was a German physician and physicist who made significant contributions in several scientific fields.
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Homogeneous coordinates
In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry.
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Homomorphism
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces).
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Hurwitz quaternion
In mathematics, a Hurwitz quaternion (or Hurwitz integer) is a quaternion whose components are either all integers or all half-integers (halves of an odd integer; a mixture of integers and half-integers is excluded).
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Hurwitz quaternion order
The Hurwitz quaternion order is a specific order in a quaternion algebra over a suitable number field.
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Hurwitz's theorem (composition algebras)
In mathematics, Hurwitz's theorem is a theorem of Adolf Hurwitz (1859–1919), published posthumously in 1923, solving the Hurwitz problem for finite-dimensional unital real non-associative algebras endowed with a positive-definite quadratic form.
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Hyperbolic quaternion
In abstract algebra, the algebra of hyperbolic quaternions is a nonassociative algebra over the real numbers with elements of the form where multiplication is determined with rules that are similar to (but different from) multiplication in the quaternions.
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Hypercomplex number
In mathematics, a hypercomplex number is a traditional term for an element of a unital algebra over the field of real numbers.
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Ian R. Porteous
Ian Robertson Porteous (9 October 1930 – 30 January 2011) was a Scottish mathematician at the University of Liverpool and an educator on Merseyside.
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Icosahedral symmetry
A regular icosahedron has 60 rotational (or orientation-preserving) symmetries, and a symmetry order of 120 including transformations that combine a reflection and a rotation.
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Icosian
In mathematics, the icosians are a specific set of Hamiltonian quaternions with the same symmetry as the 600-cell.
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Ideal (ring theory)
In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring.
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Identity element
In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.
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Imaginary unit
The imaginary unit or unit imaginary number is a solution to the quadratic equation.
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Injective function
In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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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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James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish scientist in the field of mathematical physics.
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Joachim Lambek
Joachim "Jim" Lambek (5 December 1922 – 23 June 2014) was Peter Redpath Emeritus Professor of Pure Mathematics at McGill University, where he earned his Ph.D. degree in 1950 with Hans Zassenhaus as advisor.
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John C. Baez
John Carlos Baez (born June 12, 1961) is an American mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California.
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John Horton Conway
John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
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Josiah Willard Gibbs
Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American scientist who made important theoretical contributions to physics, chemistry, and mathematics.
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Julia set
In the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets (Julia 'laces' and Fatou 'dusts') defined from a function.
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Kinematics
Kinematics is a branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the mass of each or the forces that caused the motion.
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Laplace–Runge–Lenz vector
In classical mechanics, the Laplace–Runge–Lenz vector (or simply the LRL vector) is a vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another, such as a planet revolving around a star.
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Lattice (group)
In geometry and group theory, a lattice in \mathbbR^n is a subgroup of the additive group \mathbb^n which is isomorphic to the additive group \mathbbZ^n, and which spans the real vector space \mathbb^n.
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Lénárt sphere
A Lénárt sphere is a teaching and educational research model for spherical geometry.
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Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
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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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Longman
Longman, commonly known as Pearson Longman, is a publishing company founded in London, England, in 1724 and is owned by Pearson PLC.
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Lorentz group
In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (nongravitational) physical phenomena.
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Ludwik Silberstein
Ludwik Silberstein (1872 – 1948) was a Polish-American physicist who helped make special relativity and general relativity staples of university coursework.
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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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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 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 ring
In abstract algebra, a matrix ring is any collection of matrices over some ring R that form a ring under matrix addition and matrix multiplication.
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Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
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Maynooth University
The National University of Ireland, Maynooth (NUIM; Ollscoil na hÉireann Mhá Nuad), commonly known as Maynooth University (MU), is a constituent university of the National University of Ireland in Maynooth, County Kildare, Ireland.
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Mechanics
Mechanics (Greek μηχανική) is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.
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Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
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Michiel Hazewinkel
Michiel Hazewinkel (born 22 June 1943) is a Dutch mathematician, and Emeritus Professor of Mathematics at the Centre for Mathematics and Computer and the University of Amsterdam, particularly known for his 1978 book Formal groups and applications and as editor of the Encyclopedia of Mathematics.
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Molecular dynamics
Molecular dynamics (MD) is a computer simulation method for studying the physical movements of atoms and molecules.
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Morgan Kaufmann Publishers
Morgan Kaufmann Publishers is a Burlington, Massachusetts (San Francisco, California until 2008) based publisher specializing in computer science and engineering content.
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Multiplication table
In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.
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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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Murray Gell-Mann
Murray Gell-Mann (born September 15, 1929) is an American physicist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles.
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National Council of Teachers of Mathematics
The National Council of Teachers of Mathematics (NCTM) was founded in 1920.
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Non-associative algebra
A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative.
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Noncommutative ring
In mathematics, more specifically abstract algebra and ring theory, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exists a and b in R with a·b ≠ b·a.
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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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Number
A number is a mathematical object used to count, measure and also label.
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Number theory
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
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Octahedron
In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.
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Octonion
In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are three lower-dimensional normed division algebras over the reals: the real numbers R themselves, the complex numbers C, and the quaternions H. The octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension.
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Olinde Rodrigues
Olinde Rodrigues Benjamin Olinde Rodrigues (6 October 1795 – 17 December 1851), more commonly known as Olinde Rodrigues, was a French banker, mathematician, and social reformer.
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Oliver Heaviside
Oliver Heaviside FRS (18 May 1850 – 3 February 1925) was an English self-taught electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques for the solution of differential equations (equivalent to Laplace transforms), reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis.
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Orbital mechanics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft.
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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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Patrick du Val
Patrick du Val (March 26, 1903 – January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity.
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Pauli matrices
In mathematical physics and mathematics, the Pauli matrices are a set of three complex matrices which are Hermitian and unitary.
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Peter Tait (physicist)
Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Plane (geometry)
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
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Plate trick
In mathematics and physics, the plate trick, also known as Dirac's string trick, the belt trick, Balinese cup trick, is any of several demonstrations of the mathematical theorem that SU(2) (which double-covers SO(3)) is simply connected.
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Point (geometry)
In modern mathematics, a point refers usually to an element of some set called a space.
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Point groups in three dimensions
In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere.
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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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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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PostScript
PostScript (PS) is a page description language in the electronic publishing and desktop publishing business.
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Potential
Potential generally refers to a currently unrealized ability.
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Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University.
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Pseudovector
In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation, but in three dimensions gains an additional sign flip under an improper rotation such as a reflection.
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Pure mathematics
Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts.
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Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.
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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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Quaternion group
In group theory, the quaternion group Q8 (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to a certain eight-element subset of the quaternions under multiplication.
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Quaternion Society
A scientific society, the Quaternion Society was an "International Association for Promoting the Study of Quaternions and Allied Systems of Mathematics".
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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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Quaternionic matrix
A quaternionic matrix is a matrix whose elements are quaternions.
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Quaternionic projective space
In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates lie in the ring of quaternions H. Quaternionic projective space of dimension n is usually denoted by and is a closed manifold of (real) dimension 4n.
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Quaternions and spatial rotation
Unit quaternions, also known as versors, provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions.
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Quotient
In arithmetic, a quotient (from quotiens "how many times", pronounced) is the quantity produced by the division of two numbers.
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Quotient ring
In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient groups of group theory and the quotient spaces of linear algebra.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Regular icosahedron
In geometry, a regular icosahedron is a convex polyhedron with 20 faces, 30 edges and 12 vertices.
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Rigid body
In physics, a rigid body is a solid body in which deformation is zero or so small it can be neglected.
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Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
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Robotics
Robotics is an interdisciplinary branch of engineering and science that includes mechanical engineering, electronics engineering, computer science, and others.
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Rotation (mathematics)
Rotation in mathematics is a concept originating in geometry.
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Rotation group SO(3)
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space R3 under the operation of composition.
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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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Rotations in 4-dimensional Euclidean space
In mathematics, the group of rotations about a fixed point in four-dimensional Euclidean space is denoted SO(4).
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Rotor (mathematics)
A rotor is an object in geometric algebra (or more generally Clifford algebra) that rotates any blade or general multivector about the origin.
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Royal Canal
The Royal Canal (An Chanáil Ríoga) is a canal originally built for freight and passenger transportation from the River Liffey in Dublin to Longford in Ireland.
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Royal Irish Academy
The Royal Irish Academy (RIA) (Acadamh Ríoga na hÉireann), based in Dublin, is an all-Ireland independent academic body that promotes study and excellence in the sciences, and humanities and social sciences.
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Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.
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Sedenion
In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the reals obtained by applying the Cayley–Dickson construction to the octonions.
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SIGGRAPH
SIGGRAPH (Special Interest Group on Computer GRAPHics and Interactive Techniques) is the annual conference on computer graphics (CG) convened by the ACM SIGGRAPH organization.
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Signal processing
Signal processing concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon", such as sound, images, and biological measurements.
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Simple algebra
In mathematics, specifically in ring theory, an algebra is simple if it contains no non-trivial two-sided ideals and the multiplication operation is not zero (that is, there is some a and some b such that). The second condition in the definition precludes the following situation; consider the algebra with the usual matrix operations: \left\ This is a one-dimensional algebra in which the product of any two elements is zero.
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Slerp
In computer graphics, Slerp is shorthand for spherical linear interpolation, introduced by Ken Shoemake in the context of quaternion interpolation for the purpose of animating 3D rotation.
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Space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction.
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Space group
In mathematics, physics and chemistry, a space group is the symmetry group of a configuration in space, usually in three dimensions.
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Spacetime
In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.
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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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Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
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Spin (physics)
In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei.
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Spin group
In mathematics the spin group Spin(n) is the double cover of the special orthogonal group, such that there exists a short exact sequence of Lie groups (with) As a Lie group, Spin(n) therefore shares its dimension,, and its Lie algebra with the special orthogonal group.
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Split-biquaternion
In mathematics, a split-biquaternion is a hypercomplex number of the form where w, x, y, and z are split-complex numbers and i, j, and k multiply as in the quaternion group.
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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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Steven Weinberg
Steven Weinberg (born May 3, 1933) is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles.
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Subring
In mathematics, a subring of R is a subset of a ring that is itself a ring when binary operations of addition and multiplication on R are restricted to the subset, and which shares the same multiplicative identity as R. For those who define rings without requiring the existence of a multiplicative identity, a subring of R is just a subset of R that is a ring for the operations of R (this does imply it contains the additive identity of R).
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Tensor
In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.
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Tesseract
In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.
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Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.
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Texture (crystalline)
In materials science, texture is the distribution of crystallographic orientations of a polycrystalline sample (it is also part of the geological fabric).
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Thomas precession
In physics, the Thomas precession, named after Llewellyn Thomas, is a relativistic correction that applies to the spin of an elementary particle or the rotation of a macroscopic gyroscope and relates the angular velocity of the spin of a particle following a curvilinear orbit to the angular velocity of the orbital motion.
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Three-dimensional space
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).
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Tomb Raider
Tomb Raider, also known as Lara Croft: Tomb Raider between 2001 and 2007, is a media franchise that originated with an action-adventure video game series created by British gaming company Core Design.
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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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Truncated 24-cells
In geometry, a truncated 24-cell is a uniform 4-polytope (4-dimensional uniform polytope) formed as the truncation of the regular 24-cell.
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Unicode
Unicode is a computing industry standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems.
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Unit sphere
In mathematics, a unit sphere is the set of points of distance 1 from a fixed central point, where a generalized concept of distance may be used; a closed unit ball is the set of points of distance less than or equal to 1 from a fixed central point.
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Unitary matrix
In mathematics, a complex square matrix is unitary if its conjugate transpose is also its inverse—that is, if where is the identity matrix.
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University of Dublin
The University of Dublin (Ollscoil Átha Cliath), corporately designated the Chancellor, Doctors and Masters of the University of Dublin, is a university located in Dublin, Ireland.
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Vector calculus
Vector calculus, or vector analysis, is a branch of mathematics concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3.
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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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Versor
In mathematics, a versor is a quaternion of norm one (a unit quaternion).
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Wilhelm Blaschke
Wilhelm Johann Eugen Blaschke (13 September 1885 – 17 March 1962) was an Austrian differential and integral geometer.
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William Edwin Hamilton
William Edwin Hamilton (10 May 1834 – 17 March 1902) was the elder son of the Irish mathematician Sir William Rowan Hamilton and Lady Helen Maria Hamilton Bayly.
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William Rowan Hamilton
Sir William Rowan Hamilton MRIA (4 August 1805 – 2 September 1865) was an Irish mathematician who made important contributions to classical mechanics, optics, and algebra.
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William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin, (26 June 1824 – 17 December 1907) was a Scots-Irish mathematical physicist and engineer who was born in Belfast in 1824.
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Zero divisor
In abstract algebra, an element of a ring is called a left zero divisor if there exists a nonzero such that, or equivalently if the map from to that sends to is not injective.
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2 × 2 real matrices
In mathematics, the associative algebra of real matrices is denoted by M(2, R).
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24-cell
In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
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3-sphere
In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.
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3D computer graphics
3D computer graphics or three-dimensional computer graphics, (in contrast to 2D computer graphics) are graphics that use a three-dimensional representation of geometric data (often Cartesian) that is stored in the computer for the purposes of performing calculations and rendering 2D images.
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600-cell
In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
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References
[1] https://en.wikipedia.org/wiki/Quaternion
