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Coxeter group (3,422 words) [view diff] no match in snippet view article find links to article

In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic

Numerical linear algebra (2,463 words) [view diff] no match in snippet view article find links to article

linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and

Translation (geometry) (1,675 words) [view diff] no match in snippet view article

group. A translation is an affine transformation with no fixed points. Matrix multiplications always have the origin as a fixed point. Nevertheless, there

The Matrix Reloaded (4,739 words) [view diff] no match in snippet view article find links to article

The Matrix Reloaded is a 2003 American science-fiction action film written and directed by the Wachowskis. It is the sequel to The Matrix (1999) and the

Affine transformation (3,526 words) [view diff] no match in snippet view article find links to article

transformation is invertible, the square matrix A{\displaystyle A} appearing in its matrix representation is invertible. The matrix representation of the inverse

Commutative property (2,208 words) [view diff] no match in snippet view article find links to article

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many

G2 (mathematics) (1,940 words) [view diff] no match in snippet view article

In mathematics, G2 is three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras g2,{\displaystyle {\mathfrak

Rotation (mathematics) (3,043 words) [view diff] no match in snippet view article

Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe

Polynomial (7,747 words) [view diff] no match in snippet view article find links to article

(2009) [1982]. Matrix Polynomials. Classics in Applied Mathematics. Vol. 58. Lancaster, PA: Society for Industrial and Applied Mathematics. ISBN 978-0-89871-681-8

Matrix norm (4,227 words) [view diff] no match in snippet view article find links to article

such norms are referred to as matrix norms. Matrix norms differ from vector norms in that they must also interact with matrix multiplication. Given a field

Subtraction (3,128 words) [view diff] no match in snippet view article find links to article

steps to the right to reach c. This movement to the right is modeled mathematically by addition: a + b = c. From c, it takes b steps to the left to get

Polynomial (7,747 words) [view diff] no match in snippet view article find links to article

(2009) [1982]. Matrix Polynomials. Classics in Applied Mathematics. Vol. 58. Lancaster, PA: Society for Industrial and Applied Mathematics. ISBN 978-0-89871-681-8

Quadratic form (4,379 words) [view diff] no match in snippet view article find links to article

fields, the modular group, and other areas of mathematics have been further elucidated. Any n × n matrix A determines a quadratic form qA in n variables

Iterative method (1,379 words) [view diff] no match in snippet view article find links to article

In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate

Canonical form (1,868 words) [view diff] no match in snippet view article find links to article

In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical

Unit (ring theory) (1,479 words) [view diff] no match in snippet view article

ring, in expressions like ring with a unit or unit ring, and also unit matrix. Because of this ambiguity, 1 is more commonly called the "unity" or the

Cartesian coordinate system (5,303 words) [view diff] no match in snippet view article find links to article

Descartes, whose invention of them in the 17th century revolutionized mathematics by allowing the expression of problems of geometry in terms of algebra

Terence Tao (6,531 words) [view diff] no match in snippet view article find links to article

(2012). Topics in random matrix theory (PDF). Graduate Studies in Mathematics. Vol. 132. Providence, RI: American Mathematical Society. doi:10.1090/gsm/132

Critical point (mathematics) (2,942 words) [view diff] no match in snippet view article

In mathematics, a critical point is the argument of a function where the function derivative is zero (or undefined, as specified below). The value of

Remainder (1,357 words) [view diff] no match in snippet view article find links to article

In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after

E7 (mathematics) (2,577 words) [view diff] no match in snippet view article

In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133;

Deformation (mathematics) (3,810 words) [view diff] no match in snippet view article

In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions

Hypergraph (6,128 words) [view diff] no match in snippet view article find links to article

In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge

Special functions (1,452 words) [view diff] no match in snippet view article find links to article

functions. The NIST Digital Library of Mathematical Functions has a section covering several special functions of matrix arguments. George Andrews Richard

Recurrence relation (3,866 words) [view diff] no match in snippet view article find links to article

In mathematics, a recurrence relation is an equation according to which the n{\displaystyle n}th term of a sequence of numbers is equal to some combination

Variance (9,191 words) [view diff] no match in snippet view article find links to article

)\right]=\operatorname {tr} (C),} which is the trace of the covariance matrix. Mathematics portal Look up variance in Wiktionary, the free dictionary. Bhatia–Davis

E6 (mathematics) (3,682 words) [view diff] no match in snippet view article

In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras e6{\displaystyle {\mathfrak {e}}_{6}}

Bilinear form (2,667 words) [view diff] no match in snippet view article find links to article

en}. The n × n matrix A, defined by Aij = B(ei, ej) is called the matrix of the bilinear form on the basis {e1, …, en}. If the n × 1 matrix x represents

Linear least squares (5,055 words) [view diff] no match in snippet view article find links to article

residuals. Numerical methods for linear least squares include inverting the matrix of the normal equations and orthogonal decomposition methods. Consider the

Discretization (2,204 words) [view diff] no match in snippet view article find links to article

In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts

Validated numerics (1,339 words) [view diff] no match in snippet view article find links to article

Japan Journal of Applied Mathematics, 1(1), 157. Oishi, S., & Rump, S. M. (2002). Fast verification of solutions of matrix equations. Numerische Mathematik

Permanent (mathematics) (4,112 words) [view diff] no match in snippet view article

In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant. The permanent, as well as the determinant,

List of numerical-analysis software (2,457 words) [view diff] no match in snippet view article find links to article

various programming environments. O-Matrix is a proprietary licensed matrix programming language for mathematics, engineering, science, and financial

Coefficient (1,024 words) [view diff] no match in snippet view article find links to article

In mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or an expression. It may be a number (dimensionless)

SIAM Journal on Discrete Mathematics (132 words) [view diff] no match in snippet view article find links to article

articles on pure and applied discrete mathematics. It was established in 1988, along with the SIAM Journal on Matrix Analysis and Applications, to replace

Least-squares spectral analysis (3,317 words) [view diff] no match in snippet view article find links to article

Mathematically, FOS uses a slightly modified Cholesky decomposition in a mean-square error reduction (MSER) process, implemented as a sparse matrix inversion

Seifert surface (1,328 words) [view diff] no match in snippet view article find links to article

In mathematics, a Seifert surface (named after German mathematician Herbert Seifert) is an orientable surface whose boundary is a given knot or link.

Normal operator (1,380 words) [view diff] no match in snippet view article find links to article

In mathematics, especially functional analysis, a normal operator on a complex Hilbert space H is a continuous linear operator N : H → H that commutes

Kac–Moody algebra (2,358 words) [view diff] no match in snippet view article find links to article

can be defined by generators and relations through a generalized Cartan matrix. These algebras form a generalization of finite-dimensional semisimple Lie

Rotation formalisms in three dimensions (11,148 words) [view diff] no match in snippet view article find links to article

interval [−π, π]3. Whether all mathematical solutions apply for a given application depends on the situation. The rotation matrix A is generated from the 3-2-1

Series (mathematics) (9,210 words) [view diff] no match in snippet view article

Society for Industrial and Applied Mathematics. Higham, N. J. (2009). The scaling and squaring method for the matrix exponential revisited. SIAM review

Degenerate distribution (741 words) [view diff] no match in snippet view article find links to article

In mathematics, a degenerate distribution is, according to some, a probability distribution in a space with support only on a manifold of lower dimension

Positive definiteness (145 words) [view diff] no match in snippet view article find links to article

In mathematics, positive definiteness is a property of any object to which a bilinear form or a sesquilinear form may be naturally associated, which is

Symmetry in mathematics (2,770 words) [view diff] no match in snippet view article find links to article

geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set

Conformal map (2,498 words) [view diff] no match in snippet view article find links to article

In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U{\displaystyle U} and V{\displaystyle

Incidence (geometry) (1,618 words) [view diff] no match in snippet view article

\x_{2}&y_{2}&z_{2}\end{matrix}}\right)\left({\begin{matrix}a\\b\\c\end{matrix}}\right)=\left({\begin{matrix}0\\0\\0\end{matrix}}\right).} This system

Graph (abstract data type) (1,733 words) [view diff] no match in snippet view article

graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set

Logarithm (11,494 words) [view diff] no match in snippet view article find links to article

in many areas of mathematics and its inverse function is often referred to as the logarithm. For example, the logarithm of a matrix is the (multi-valued)

En (Lie algebra) (1,195 words) [view diff] no match in snippet view article

In mathematics, especially in Lie theory, En is the Kac–Moody algebra whose Dynkin diagram is a bifurcating graph with three branches of length 1, 2 and

Kernel (373 words) [view diff] no match in snippet view article find links to article

stochastic discount factor used in mathematical finance Positive-definite kernel, a generalization of a positive-definite matrix Kernel trick, in statistics

Computational mechanics (604 words) [view diff] no match in snippet view article find links to article

mechanics (CM) is interdisciplinary. Its three pillars are mechanics, mathematics, and computer science and physics. Computational fluid dynamics, computational

Total least squares (3,042 words) [view diff] no match in snippet view article find links to article

with m>n. X is a m×n matrix whose elements are either constants or functions of the independent variables, x. The weight matrix W is, ideally, the inverse

Alan Edelman (763 words) [view diff] no match in snippet view article find links to article

random matrix theory. He is one of the creators of the technical programming language Julia. Edelman received B.S. and M.S. degrees in mathematics from

Vector flow (637 words) [view diff] no match in snippet view article find links to article

In mathematics, the vector flow refers to a set of closely related concepts of the flow determined by a vector field. These appear in a number of different

Numerical analysis (3,871 words) [view diff] no match in snippet view article find links to article

Mathematica: Mathematical Problems for Ordinary Differential Equations. Springer. ISBN 978-0-8176-4205-1. Golub, Gene H.; Charles F. Van Loan (1986). Matrix Computations

Spectral graph theory (1,745 words) [view diff] no match in snippet view article find links to article

such as its adjacency matrix or Laplacian matrix. The adjacency matrix of a simple undirected graph is a real symmetric matrix and is therefore orthogonally

Kernel method (1,633 words) [view diff] no match in snippet view article find links to article

machines is infinite dimensional but only requires a finite dimensional matrix from user-input according to the Representer theorem. Kernel machines are

Trace (linear algebra) (5,102 words) [view diff] no match in snippet view article

In linear algebra, the trace of a square matrix A, denoted tr(A), is defined to be the sum of elements on the main diagonal (from the upper left to the

Correlation (4,969 words) [view diff] no match in snippet view article find links to article

one wants to find the "nearest" correlation matrix to an "approximate" correlation matrix (e.g., a matrix which typically lacks semi-definite positiveness

Metric signature (1,273 words) [view diff] no match in snippet view article find links to article

criterion, a symmetric matrix is positive-definite if and only if all the determinants of its main minors are positive. In mathematics, the usual convention

Pascal's triangle (7,603 words) [view diff] no match in snippet view article find links to article

1\\1\quad 7\quad 21\quad 35\quad 35\quad 21\quad 7\quad 1\end{array}}} In mathematics, Pascal's triangle is a triangular array of the binomial coefficients

Stirling numbers of the first kind (6,700 words) [view diff] no match in snippet view article find links to article

In mathematics, especially in combinatorics, Stirling numbers of the first kind arise in the study of permutations. In particular, the Stirling numbers

Gene H. Golub (1,805 words) [view diff] no match in snippet view article find links to article

in mathematics. His M.A. degree was more specifically in Mathematical Statistics. His PhD dissertation was entitled "The Use of Chebyshev Matrix Polynomials

List of calculus topics (389 words) [view diff] no match in snippet view article find links to article

This is a list of calculus topics. Limit (mathematics) Limit of a function One-sided limit Limit of a sequence Indeterminate form Orders of approximation

List of partition topics (237 words) [view diff] no match in snippet view article find links to article

partition of an interval, partition of unity, partition of a matrix; see block matrix, and partition of the sum of squares in statistics problems, especially

Submersion (mathematics) (1,569 words) [view diff] no match in snippet view article

In mathematics, a submersion is a differentiable map between differentiable manifolds whose differential is everywhere surjective. This is a basic concept

Relation (mathematics) (3,693 words) [view diff] no match in snippet view article

In mathematics, a relation on a set may, or may not, hold between two given members of the set. As an example, "is less than" is a relation on the set

Pseudovector (3,968 words) [view diff] no match in snippet view article find links to article

active transformations.) Mathematically, if everything in the universe undergoes a rotation described by a rotation matrix R, so that a displacement

Orthogonal group (7,820 words) [view diff] no match in snippet view article find links to article

matrices, where the group operation is given by matrix multiplication (an orthogonal matrix is a real matrix whose inverse equals its transpose). The orthogonal

Multiplicative inverse (2,267 words) [view diff] no match in snippet view article find links to article

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

Directed acyclic graph (5,623 words) [view diff] no match in snippet view article find links to article

In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is,

Latin square (3,514 words) [view diff] no match in snippet view article find links to article

example of a 3×3 Latin square is The name "Latin square" was inspired by mathematical papers by Leonhard Euler (1707–1783), who used Latin characters as symbols

Homogeneous relation (2,177 words) [view diff] no match in snippet view article find links to article

In mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian

Range (514 words) [view diff] no match in snippet view article find links to article

space, also called the range of a matrix, is the set of all possible linear combinations of the column vectors of the matrix Projective range, a line or a

Galerkin method (2,790 words) [view diff] no match in snippet view article find links to article

In mathematics, in the area of numerical analysis, Galerkin methods are named after the Soviet mathematician Boris Galerkin. They convert a continuous

Regularization (mathematics) (4,220 words) [view diff] no match in snippet view article

In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is a process that changes

List of Martin Gardner Mathematical Games columns (355 words) [view diff] no match in snippet view article find links to article

1957 – December 1980), Martin Gardner wrote 288 consecutive monthly "Mathematical Games" columns for Scientific American magazine. During the next 5+1⁄2

Google matrix (1,773 words) [view diff] no match in snippet view article find links to article

A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links

Digital image processing (4,707 words) [view diff] no match in snippet view article find links to article

transformations can be combined into a single matrix, thus allowing rotation around any point in the image. Mathematical morphology is suitable for denoising images

Unit fraction (2,858 words) [view diff] no match in snippet view article find links to article

The Mathematical Intelligencer, 5 (3): 75–76, doi:10.1007/bf03026580, S2CID 122191726 Choi, Man Duen (1983), "Tricks or treats with the Hilbert matrix",

Rajendra Bhatia (355 words) [view diff] no match in snippet view article find links to article

Perturbation Bounds for Matrix Eigenvalues. Longman. Bhatia, Rajendra (1997). Matrix Analysis. Springer, Graduate Texts in Mathematics. Bhatia, Rajendra (2007)

Exponential (235 words) [view diff] no match in snippet view article find links to article

to any of several mathematical topics related to exponentiation, including: Exponential function, also: Matrix exponential, the matrix analogue to the above

Arthur Cayley (2,025 words) [view diff] no match in snippet view article find links to article

well as mathematics. He worked as a lawyer for 14 years. He postulated what is now known as the Cayley–Hamilton theorem—that every square matrix is a root

Algebraic number field (8,026 words) [view diff] no match in snippet view article find links to article

In mathematics, an algebraic number field (or simply number field) is an extension field K{\displaystyle K} of the field of rational numbers Q{\displaystyle

Homogeneous coordinates (3,308 words) [view diff] no match in snippet view article find links to article

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, are

Peter–Weyl theorem (2,408 words) [view diff] no match in snippet view article find links to article

In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are

Killing form (1,777 words) [view diff] no match in snippet view article find links to article

In mathematics, the Killing form, named after Wilhelm Killing, is a symmetric bilinear form that plays a basic role in the theories of Lie groups and

Computational complexity of mathematical operations (1,481 words) [view diff] no match in snippet view article find links to article

Applied Mathematics. doi:10.1137/1.9781611975031.67. ISBN 978-1-61197-503-1. S2CID 33396059. Knight, Philip A. (May 1995). "Fast rectangular matrix multiplication

Rotation (3,840 words) [view diff] no match in snippet view article find links to article

such a direction is the question of existence of an eigenvector for the matrix A representing the rotation. Every 2D rotation around the origin through

Minimax (3,719 words) [view diff] no match in snippet view article find links to article

consider the payoff matrix for A displayed on the table ("Payoff matrix for player A"). Assume the payoff matrix for B is the same matrix with the signs reversed

Nth root (4,699 words) [view diff] no match in snippet view article find links to article

In mathematics, taking the nth root is an operation involving two numbers, the radicand and the index or degree. Taking the nth root is written as xn{\displaystyle

Algebraic number field (8,026 words) [view diff] no match in snippet view article find links to article

In mathematics, an algebraic number field (or simply number field) is an extension field K{\displaystyle K} of the field of rational numbers Q{\displaystyle

Google matrix (1,773 words) [view diff] no match in snippet view article find links to article

A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links

Lax pair (1,633 words) [view diff] no match in snippet view article find links to article

In mathematics, in the theory of integrable systems, a Lax pair is a pair of time-dependent matrices or operators that satisfy a corresponding differential

List of numerical analysis topics (8,342 words) [view diff] no match in snippet view article find links to article

analysis: Sparse matrix Band matrix Bidiagonal matrix Tridiagonal matrix Pentadiagonal matrix Skyline matrix Circulant matrix Triangular matrix Diagonally dominant

Bipartite graph (4,073 words) [view diff] no match in snippet view article find links to article

In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets

Symmetric bilinear form (1,443 words) [view diff] no match in snippet view article find links to article

In mathematics, a symmetric bilinear form on a vector space is a bilinear map from two copies of the vector space to the field of scalars such that the

Converse relation (1,678 words) [view diff] no match in snippet view article find links to article

In mathematics, the converse of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example

Knuth's up-arrow notation (3,242 words) [view diff] no match in snippet view article find links to article

In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. In his 1947 paper, R. L

List of mathematical theories (215 words) [view diff] no match in snippet view article find links to article

This is a list of mathematical theories. Almgren–Pitts min-max theory Approximation theory Arakelov theory Artin–Schreier theory Asymptotic theory Automata

Latent semantic analysis (7,347 words) [view diff] no match in snippet view article find links to article

This matrix is also common to standard semantic models, though it is not necessarily explicitly expressed as a matrix, since the mathematical properties

Symplectic group (2,943 words) [view diff] no match in snippet view article find links to article

Symplectic matrix, Symplectic vector space, Symplectic representation Unitary group Θ10 "Symplectic group", Encyclopedia of Mathematics Retrieved on

Ordered Bell number (2,247 words) [view diff] no match in snippet view article find links to article

Discrete Mathematics, 5 (4): 497–499, doi:10.1137/0405040, MR 1186818 Lewis, Barry (2010), "Revisiting the Pascal matrix", American Mathematical Monthly

Number line (2,414 words) [view diff] no match in snippet view article find links to article

form of real products with the identity matrix in the ring. Cantor–Dedekind axiom Imaginary line (mathematics) Line (geometry) Projectively extended real

Unit vector (1,732 words) [view diff] no match in snippet view article find links to article

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

Graph (discrete mathematics) (3,667 words) [view diff] no match in snippet view article

In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects

Short division (1,025 words) [view diff] no match in snippet view article find links to article

partial dividend (9). 24)9150¯{\displaystyle {\begin{matrix}2\\4{\overline {)9^{1}50}}\end{matrix}}} Next one repeats step 2, using the small digit concatenated

Principia Mathematica (9,458 words) [view diff] no match in snippet view article find links to article

(often abbreviated PM) is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand

Scientific Research Publishing (1,208 words) [view diff] no match in snippet view article find links to article

different from their own. In 2012, one of its journals, Advances in Pure Mathematics, accepted a paper written by a parody generator; the paper was not published

Stable manifold theorem (367 words) [view diff] no match in snippet view article find links to article

In mathematics, especially in the study of dynamical systems and differential equations, the stable manifold theorem is an important result about the

Conjugation (404 words) [view diff] no match in snippet view article find links to article

degree Conjugate transpose, the complex conjugate of the transpose of a matrix Harmonic conjugate in complex analysis Conjugate (graph theory), an alternative

GAUSS (software) (165 words) [view diff] no match in snippet view article

GAUSS is a matrix programming language for mathematics and statistics, developed and marketed by Aptech Systems. Its primary purpose is the solution of

Catalan number (5,473 words) [view diff] no match in snippet view article find links to article

In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively

Heinz mean (301 words) [view diff] no match in snippet view article find links to article

v t e In mathematics, the Heinz mean (named after E. Heinz) of two non-negative real numbers A and B, was defined by Bhatia as: Hx⁡(A,B)=AxB1−x+A1−xBx2

Alternating-direction implicit method (3,234 words) [view diff] no match in snippet view article find links to article

iterative method used to solve Sylvester matrix equations. It is a popular method for solving the large matrix equations that arise in systems theory and

Simple ring (902 words) [view diff] no match in snippet view article find links to article

In abstract algebra, a branch of mathematics, a simple ring is a non-zero ring that has no two-sided ideal besides the zero ideal and itself. In particular

GAUSS (software) (165 words) [view diff] no match in snippet view article

GAUSS is a matrix programming language for mathematics and statistics, developed and marketed by Aptech Systems. Its primary purpose is the solution of

Algebraic group (2,209 words) [view diff] no match in snippet view article find links to article

In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety

Jonathan Keating (503 words) [view diff] no match in snippet view article find links to article

has made contributions to applied mathematics and mathematical physics, in particular to quantum chaos, random matrix theory and number theory. He read

Normal (570 words) [view diff] no match in snippet view article find links to article

function, in set theory Normal invariants, in geometric topology Normal matrix, a matrix that commutes with its conjugate transpose Normal measure, in set theory

Frank Harary (2,485 words) [view diff] no match in snippet view article find links to article

adjacency matrix for the tree T and check that it is indeed the tree which we sought. Squaring the adjacency matrix of T should yield an adjacency matrix for

Mathematical formulation of quantum mechanics (7,860 words) [view diff] no match in snippet view article find links to article

the mathematics of the new quantum mechanics was already laid out in it. It is also said that Heisenberg had consulted Hilbert about his matrix mechanics

Orbital state vectors (826 words) [view diff] no match in snippet view article find links to article

Position-Velocity vectors, Two-line element set (TLE), and Vector Covariance Matrix (VCM). State vectors are defined with respect to some frame of reference

Riemann's differential equation (1,073 words) [view diff] no match in snippet view article find links to article

In mathematics, Riemann's differential equation, named after Bernhard Riemann, is a generalization of the hypergeometric differential equation, allowing

List of mathematical identities (168 words) [view diff] no match in snippet view article find links to article

This article lists mathematical identities, that is, identically true relations holding in mathematics. Bézout's identity (despite its usual name, it

Permutation (10,966 words) [view diff] no match in snippet view article find links to article

In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered

Spherical coordinate system (6,282 words) [view diff] no match in snippet view article find links to article

sphere of dimension n (mathematics)Pages displaying short descriptions of redirect targets Jacobian matrix and determinant – Matrix of all first-order partial

Backslash (2,111 words) [view diff] no match in snippet view article find links to article

The backslash \ is a mark used mainly in computing and mathematics. It is the mirror image of the common slash /. It is a relatively recent mark, first

Algebraic logic (2,210 words) [view diff] no match in snippet view article find links to article

In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic

Kinematics (8,213 words) [view diff] no match in snippet view article find links to article

Kinematics is a subfield of physics and mathematics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems

Quaternion algebra (1,488 words) [view diff] no match in snippet view article find links to article

over F that has dimension 4 over F. Every quaternion algebra becomes a matrix algebra by extending scalars (equivalently, tensoring with a field extension)

Basic hypergeometric series (2,045 words) [view diff] no match in snippet view article find links to article

of the American Mathematical Society 131, pp. 719–724 Ahmed Salem (2014) The basic Gauss hypergeometric matrix function and its matrix q-difference equation

Quantum group (4,637 words) [view diff] no match in snippet view article find links to article

type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras), and

Polynomial regression (2,195 words) [view diff] no match in snippet view article find links to article

_{m}x_{i}^{m}+\varepsilon _{i}\ (i=1,2,\dots ,n)} can be expressed in matrix form in terms of a design matrix X{\displaystyle \mathbf {X} }, a response vector y→{\displaystyle

Spectral gap (75 words) [view diff] no match in snippet view article find links to article

In mathematics, the spectral gap is the difference between the moduli of the two largest eigenvalues of a matrix or operator; alternately, it is sometimes

Convolution (8,260 words) [view diff] no match in snippet view article find links to article

In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions (f{\displaystyle f} and g{\displaystyle

Levenberg–Marquardt algorithm (3,093 words) [view diff] no match in snippet view article find links to article

In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve

Fulkerson Prize (1,852 words) [view diff] no match in snippet view article find links to article

the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to

Norm (489 words) [view diff] no match in snippet view article find links to article

length or size to any vector in a vector space Matrix norm, a map that assigns a length or size to a matrix Operator norm, a map that assigns a length or

Norm (489 words) [view diff] no match in snippet view article find links to article

length or size to any vector in a vector space Matrix norm, a map that assigns a length or size to a matrix Operator norm, a map that assigns a length or

Nilpotent (1,145 words) [view diff] no match in snippet view article find links to article

In mathematics, an element x{\displaystyle x} of a ring R{\displaystyle R} is called nilpotent if there exists some positive integer n{\displaystyle n}

Convolution (8,260 words) [view diff] no match in snippet view article find links to article

In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions (f{\displaystyle f} and g{\displaystyle

Pseudospectrum (308 words) [view diff] no match in snippet view article find links to article

non-normal operators and their eigenfunctions. The ε-pseudospectrum of a matrix A consists of all eigenvalues of matrices which are ε-close to A: Λϵ(A)={λ∈C∣∃x∈Cn∖{0}

Spectrum (949 words) [view diff] no match in snippet view article find links to article

neurodevelopmental disorders. In mathematics, the spectrum of a matrix is the multiset of the eigenvalues of the matrix. In functional analysis, the concept

Vector calculus (2,073 words) [view diff] no match in snippet view article find links to article

Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional

List of multivariable calculus topics (156 words) [view diff] no match in snippet view article find links to article

differential forms Contact (mathematics) Contour integral Contour line Critical point (mathematics) Curl (mathematics) Current (mathematics) Curvature Curvilinear

Algebra of physical space (1,429 words) [view diff] no match in snippet view article find links to article

In the Pauli matrix representation, the unit basis vectors are replaced by the Pauli matrices and the scalar part by the identity matrix. This means that

Nina Snaith (357 words) [view diff] no match in snippet view article find links to article

appeared in her doctoral thesis Random Matrix Theory and zeta functions. Snaith is currently Professor of Mathematical Physics at the University of Bristol

Adjoint representation (3,227 words) [view diff] no match in snippet view article find links to article

In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations

Invariant subspace (1,853 words) [view diff] no match in snippet view article find links to article

In mathematics, an invariant subspace of a linear mapping T : V → V i.e. from some vector space V to itself, is a subspace W of V that is preserved by

Complex analysis (2,485 words) [view diff] no match in snippet view article find links to article

is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic

Crunode (143 words) [view diff] no match in snippet view article find links to article

In mathematics, a crunode (archaic) or node is a point where a curve intersects itself so that both branches of the curve have distinct tangent lines

Classical group (7,156 words) [view diff] no match in snippet view article find links to article

In mathematics, the classical groups are defined as the special linear groups over the reals R, the complex numbers C and the quaternions H together with

Haar wavelet (4,139 words) [view diff] no match in snippet view article find links to article

In mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is

Incidence structure (2,484 words) [view diff] no match in snippet view article find links to article

In mathematics, an incidence structure is an abstract system consisting of two types of objects and a single relationship between these types of objects

Generator (390 words) [view diff] no match in snippet view article find links to article

Generator (mathematics) Generator matrix, a matrix used in coding theory Generator (category theory) of a category, in category mathematics Generating

History of string theory (4,181 words) [view diff] no match in snippet view article find links to article

condensed matter physics, cosmology, and pure mathematics. String theory represents an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg

Idempotence (2,877 words) [view diff] no match in snippet view article find links to article

Biordered set Closure operator Fixed point (mathematics) Idempotent of a code Idempotent analysis Idempotent matrix Idempotent relation – a generalization

Multivariate normal distribution (8,737 words) [view diff] no match in snippet view article find links to article

1≤j≤k{\displaystyle 1\leq j\leq k}. The inverse of the covariance matrix is called the precision matrix, denoted by Q=Σ−1{\displaystyle {\boldsymbol {Q}}={\boldsymbol

Matrix theory (physics) (667 words) [view diff] no match in snippet view article

In theoretical physics, the matrix theory is a quantum mechanical model proposed in 1997 by Tom Banks, Willy Fischler, Stephen Shenker, and Leonard Susskind;

Concurrent lines (1,453 words) [view diff] no match in snippet view article find links to article

only if the rank of the coefficient matrix is equal to the rank of the augmented matrix (the coefficient matrix augmented with a column of intercept

Jade Mirror of the Four Unknowns (1,918 words) [view diff] no match in snippet view article find links to article

(四元玉鉴), also referred to as Jade Mirror of the Four Origins, is a 1303 mathematical monograph by Yuan dynasty mathematician Zhu Shijie. Zhu advanced Chinese

Unitary operator (1,235 words) [view diff] no match in snippet view article find links to article

notion of a unitary operator is a generalization of the notion of a unitary matrix. Orthogonal matrices are the special case of unitary matrices in which all

Generator (390 words) [view diff] no match in snippet view article find links to article

Generator (mathematics) Generator matrix, a matrix used in coding theory Generator (category theory) of a category, in category mathematics Generating

Unitary operator (1,235 words) [view diff] no match in snippet view article find links to article

notion of a unitary operator is a generalization of the notion of a unitary matrix. Orthogonal matrices are the special case of unitary matrices in which all

Muirhead's inequality (1,170 words) [view diff] no match in snippet view article find links to article

In mathematics, Muirhead's inequality, named after Robert Franklin Muirhead, also known as the "bunching" method, generalizes the inequality of arithmetic

Surface (mathematics) (3,873 words) [view diff] no match in snippet view article

In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be

Rayleigh quotient (2,471 words) [view diff] no match in snippet view article find links to article

In mathematics, the Rayleigh quotient (/ˈreɪ.li/) for a given complex Hermitian matrix M{\displaystyle M} and nonzero vector x{\displaystyle x} is defined

Conjugate gradient method (6,697 words) [view diff] no match in snippet view article find links to article

solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite. The conjugate gradient method is often implemented

Quantum affine algebra (305 words) [view diff] no match in snippet view article find links to article

In mathematics, a quantum affine algebra (or affine quantum group) is a Hopf algebra that is a q-deformation of the universal enveloping algebra of an

Gaussian blur (2,241 words) [view diff] no match in snippet view article find links to article

scales—see scale space representation and scale space implementation. Mathematically, applying a Gaussian blur to an image is the same as convolving the

Resolvent formalism (842 words) [view diff] no match in snippet view article find links to article

In mathematics, the resolvent formalism is a technique for applying concepts from complex analysis to the study of the spectrum of operators on Banach

Alexander polynomial (2,511 words) [view diff] no match in snippet view article find links to article

In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander

Linear Algebra and Its Applications (151 words) [view diff] no match in snippet view article find links to article

its Applications is a biweekly peer-reviewed mathematics journal published by Elsevier and covering matrix theory and finite-dimensional linear algebra

List of algorithms (7,908 words) [view diff] no match in snippet view article find links to article

square matrix multiplication Freivalds' algorithm: a randomized algorithm used to verify matrix multiplication Strassen algorithm: faster matrix multiplication

Generalized method of moments (3,196 words) [view diff] no match in snippet view article find links to article

positive-definite weighting matrix, and mT{\displaystyle m^{\mathsf {T}}} denotes transposition. In practice, the weighting matrix W is computed based on the

Hamburger moment problem (1,088 words) [view diff] no match in snippet view article find links to article

In mathematics, the Hamburger moment problem, named after Hans Ludwig Hamburger, is formulated as follows: given a sequence (m0, m1, m2, ...), does there

List of graph theory topics (664 words) [view diff] no match in snippet view article find links to article

Pre-topological order Adjacency list Adjacency matrix Adjacency algebra – the algebra of polynomials in the adjacency matrix Canadian traveller problem Cliques and

Continuant (mathematics) (936 words) [view diff] no match in snippet view article

a multivariate polynomial representing the determinant of a tridiagonal matrix and having applications in generalized continued fractions. The n-th continuant

Charles Royal Johnson (590 words) [view diff] no match in snippet view article find links to article

a Class of 1961 professor of mathematics at College of William and Mary. The books Matrix Analysis and Topics in Matrix Analysis, co-written by him with

Packing dimension (979 words) [view diff] no match in snippet view article find links to article

In mathematics, the packing dimension is one of a number of concepts that can be used to define the dimension of a subset of a metric space. Packing dimension

Congruence (339 words) [view diff] no match in snippet view article find links to article

a matrix group with integer entries Congruence of squares, in number theory, a congruence commonly used in integer factorization algorithms Matrix congruence

Characteristic equation (78 words) [view diff] no match in snippet view article find links to article

equation obtained by equating to zero the characteristic polynomial of a matrix or of a linear mapping Method of characteristics, a technique for solving

Pascual Jordan (1,953 words) [view diff] no match in snippet view article find links to article

and quantum field theory. He contributed much to the mathematical form of matrix mechanics, and developed canonical anticommutation relations for fermions

Operator space (187 words) [view diff] no match in snippet view article find links to article

In functional analysis, a discipline within mathematics, an operator space is a normed vector space (not necessarily a Banach space) "given together with

Martin Gardner (9,526 words) [view diff] no match in snippet view article find links to article

1960 "Mathematical Games" column, Gardner introduced the fictitious "Dr. Matrix" and wrote about him often over the next two decades. Dr. Matrix was not

Analytic function of a matrix (2,006 words) [view diff] no match in snippet view article find links to article

In mathematics, every analytic function can be used for defining a matrix function that maps square matrices with complex entries to square matrices of

Stokes' theorem (4,405 words) [view diff] no match in snippet view article find links to article

}({\boldsymbol {\psi }})\,\mathrm {d} \gamma }} where Jyψ stands for the Jacobian matrix of ψ at y = γ(t). Now let {eu, ev} be an orthonormal basis in the coordinate

Bauer–Fike theorem (1,525 words) [view diff] no match in snippet view article find links to article

In mathematics, the Bauer–Fike theorem is a standard result in the perturbation theory of the eigenvalue of a complex-valued diagonalizable matrix. In

Singular (169 words) [view diff] no match in snippet view article find links to article

homology SINGULAR, an open source Computer Algebra System (CAS) Singular matrix, a matrix that is not invertible Singular measure, a measure or probability distribution

Schottky problem (842 words) [view diff] no match in snippet view article find links to article

In mathematics, the Schottky problem, named after Friedrich Schottky, is a classical question of algebraic geometry, asking for a characterisation of

Charles Royal Johnson (590 words) [view diff] no match in snippet view article find links to article

a Class of 1961 professor of mathematics at College of William and Mary. The books Matrix Analysis and Topics in Matrix Analysis, co-written by him with

Tracy–Widom distribution (3,523 words) [view diff] no match in snippet view article find links to article

The Tracy–Widom distribution is a probability distribution from random matrix theory introduced by Craig Tracy and Harold Widom (1993, 1994). It is the

Composition algebra (1,312 words) [view diff] no match in snippet view article find links to article

In mathematics, a composition algebra A over a field K is a not necessarily associative algebra over K together with a nondegenerate quadratic form N

Axis–angle representation (1,930 words) [view diff] no match in snippet view article find links to article

In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating

Gaussian function (4,353 words) [view diff] no match in snippet view article find links to article

In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f(x)=exp⁡(−x2){\displaystyle f(x)=\exp(-x^{2})}

Unit (693 words) [view diff] no match in snippet view article find links to article

impulse of height 1 Unit interval, an interval of distance 1 Unit matrix, a diagonal matrix such that all elements on the main diagonal are 1 and all the

Stokes' theorem (4,405 words) [view diff] no match in snippet view article find links to article

}({\boldsymbol {\psi }})\,\mathrm {d} \gamma }} where Jyψ stands for the Jacobian matrix of ψ at y = γ(t). Now let {eu, ev} be an orthonormal basis in the coordinate

Schottky problem (842 words) [view diff] no match in snippet view article find links to article

In mathematics, the Schottky problem, named after Friedrich Schottky, is a classical question of algebraic geometry, asking for a characterisation of

Alan J. Hoffman (3,693 words) [view diff] no match in snippet view article find links to article

Muriel and Jesse. Alan knew from an early age that he wanted a career in mathematics. He was a good student in all disciplines, finding inspiration in both

Crank–Nicolson method (3,328 words) [view diff] no match in snippet view article find links to article

O(N3){\displaystyle {\mathcal {O}}(N^{3})} for a full matrix, in which N{\displaystyle N} indicates the matrix size. The Crank–Nicolson method is often applied

Arf invariant of a knot (704 words) [view diff] no match in snippet view article find links to article

the surface. This means that V is a 2g × 2g matrix with the property that V − VT is a symplectic matrix. The Arf invariant of the knot is the residue

Schur decomposition (1,327 words) [view diff] no match in snippet view article find links to article

In the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition.

Riemann–Hilbert problem (3,596 words) [view diff] no match in snippet view article find links to article

V. (1992), "The isomonodromy approach to matrix models in 2D quantum gravity", Communications in Mathematical Physics, 147 (2): 395–430, Bibcode:1992CMaPh

David Wood (mathematician) (620 words) [view diff] no match in snippet view article

The Mathematical Research Institute MATRIX. Wood is an Editor-in-Chief of the Electronic Journal of Combinatorics, Editor-in-Chief of the MATRIX Book

Integral transform (1,265 words) [view diff] no match in snippet view article find links to article

In mathematics, an integral transform is a type of transform that maps a function from its original function space into another function space via integration

Iwasawa decomposition (905 words) [view diff] no match in snippet view article find links to article

In mathematics, the Iwasawa decomposition (aka KAN from its expression) of a semisimple Lie group generalises the way a square real matrix can be written

Eugene Wigner (5,098 words) [view diff] no match in snippet view article find links to article

pure mathematics, in which he authored a number of mathematical theorems. In particular, Wigner's theorem is a cornerstone in the mathematical formulation

Complement (set theory) (1,471 words) [view diff] no match in snippet view article

(X\times Y)\setminus R.} Here, R{\displaystyle R} is often viewed as a logical matrix with rows representing the elements of X,{\displaystyle X,} and columns

Stieltjes moment problem (444 words) [view diff] no match in snippet view article find links to article

In mathematics, the Stieltjes moment problem, named after Thomas Joannes Stieltjes, seeks necessary and sufficient conditions for a sequence (m0, m1,

Kent Mathematics Project (602 words) [view diff] no match in snippet view article find links to article

The Kent Mathematics Project (K.M.P.) was an educational system for teaching mathematics to 9-16 year olds. The system comprised task worksheets, booklets

Newton's method in optimization (1,759 words) [view diff] no match in snippet view article find links to article

or saddle points; see section "Several variables" in Critical point (mathematics) and also section "Geometric interpretation" in this article. This is

Hyperbolic partial differential equation (1,192 words) [view diff] no match in snippet view article find links to article

In mathematics, a hyperbolic partial differential equation of order n{\displaystyle n} is a partial differential equation (PDE) that, roughly speaking

Mathematical constant (3,442 words) [view diff] no match in snippet view article find links to article

names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as e and π occurring

List of network scientists (189 words) [view diff] no match in snippet view article find links to article

structure Edge Loop Neighborhood Path Vertex Adjacency list / matrix Incidence list / matrix Types Bipartite Complete Directed Hyper Labeled Multi Random

Norm (mathematics) (5,519 words) [view diff] no match in snippet view article

Magnitude (mathematics) – Property determining comparison and ordering Matrix norm – Norm on a vector space of matrices Minkowski distance – Mathematical metric

Rigid transformation (1,133 words) [view diff] no match in snippet view article find links to article

vectors. Matrices that satisfy this condition form a mathematical group under the operation of matrix multiplication called the orthogonal group of n×n matrices

List of mathematical topics in quantum theory (359 words) [view diff] no match in snippet view article find links to article

This is a list of mathematical topics in quantum theory, by Wikipedia page. See also list of functional analysis topics, list of Lie group topics, list

Weighted least squares (2,011 words) [view diff] no match in snippet view article find links to article

generalized least squares, when all the off-diagonal entries of the covariance matrix of the errors, are null. The fit of a model to a data point is measured

Inversion (558 words) [view diff] no match in snippet view article find links to article

Involution (mathematics), a function that is its own inverse (when applied twice, the starting value is obtained) Inversion (discrete mathematics), any item

Semigroup (4,672 words) [view diff] no match in snippet view article find links to article

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation

Schur–Horn theorem (2,661 words) [view diff] no match in snippet view article find links to article

Doubly stochastic matrices and the diagonal of a rotation matrix, American Journal of Mathematics 76 (1954), 620–630. Kadison, R. V.; Pedersen, G. K., Means

Euclidean group (2,104 words) [view diff] no match in snippet view article find links to article

In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space En{\displaystyle \mathbb {E} ^{n}}; that is, the transformations

Tripod packing (1,368 words) [view diff] no match in snippet view article find links to article

Unsolved problem in mathematics: How many tripods can have their apexes packed into a given cube? (more unsolved problems in mathematics) In combinatorics

Linear fractional transformation (1,628 words) [view diff] no match in snippet view article find links to article

originally defined on the 3 × 3 real matrix ring. Linear fractional transformations are widely used in various areas of mathematics and its applications to engineering

List of operator splitting topics (106 words) [view diff] no match in snippet view article find links to article

equations GRADELA — simple gradient elasticity model Matrix splitting — general method of splitting a matrix operator into a sum or difference of matrices Paul

Transfer matrix (1,002 words) [view diff] no match in snippet view article find links to article

In applied mathematics, the transfer matrix is a formulation in terms of a block-Toeplitz matrix of the two-scale equation, which characterizes refinable

Split-quaternion (3,110 words) [view diff] no match in snippet view article find links to article

a matrix is invertible if and only its determinant is nonzero, and, in this case, the inverse of the matrix is the quotient of the cofactor matrix by

Matrix polynomial (647 words) [view diff] no match in snippet view article find links to article

In mathematics, a matrix polynomial is a polynomial with square matrices as variables. Given an ordinary, scalar-valued polynomial P(x)=∑i=0naixi=a0+a1x+a2x2+⋯+anxn