Matrix (mathematics)

Definition

In mathematics, a matrix is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and columns, usually satisfying certain properties of addition and multiplication.

Related concepts

(0,1)-matrix 1-morphism 2-category A New English Dictionary on Historical Principles Absolute value Absorbing state Abstract index notation Academic Press Addison-Wesley Addition Additive inverse Adi Ben-Israel Adjacency matrix Adjugate matrix Affine connection Affine coordinate system Affine geometry Affine group Affine space Affine transformation Albert Einstein Alfred North Whitehead Alfred Tarski Algebra Algebra (Lang)Algebraically closed field Algorithm Alternant matrix Alternating sign matrix American Mathematical Society Angular momentum Anti-diagonal matrix Antihermitian matrix Antisymmetric tensor Apparent variable Archive for History of Exact Sciences Arrowhead matrix Arthur Cayley Asher Peres Associative algebra Associativity Asterisk Augmented matrix Augustin-Louis Cauchy Axiom Axiom of reducibility Band matrix Bareiss algorithm Bartel Leendert van der Waerden Base case (recursion)Basic Linear Algebra Subprograms Basis (linear algebra)Basis transformation matrix Bernhard Riemann Bertrand Russell Biadjacency matrix Bicategory Bidiagonal matrix Bijection Bilinear form Binary operation Bisymmetric matrix Bivector Block-diagonal matrix Block matrix Block tridiagonal matrix Boolean matrix Branch of mathematics Brian Conrey Bézout matrix Cabibbo–Kobayashi–Maskawa matrix Cambridge University Press Carl Friedrich Gauss Carl Gustav Jacob Jacobi Cartan formalism (physics)Cartan matrix Cartesian coordinate system Category (mathematics)Category of matrices Category of vector spaces Cauchy matrix Cauchy stress tensor Cauchy–Binet formula Cayley–Hamilton theorem Centering matrix Centrosymmetric matrix Change of basis Characteristic polynomial Charles F. Van Loan Charles Royal Johnson Chemical bond Chemistry Chinese mathematics Cholesky decomposition Chris Godsil Circulant matrix Classical treatment of tensors Claude Itzykson Clifford algebra Coding theory Coefficient matrix Cofactor matrix Coherency (homotopy theory)Column matrix Combinatorics Commutation matrix Commutative Commutative monoid Commutative property Commutative ring Commutative semiring Companion matrix Comparison of linear algebra libraries Complex Hadamard matrix Complex conjugate Complex number Complexity analysis Component-free treatment of tensors Computer algebra system Computer graphics Computer vision Condition number Conference matrix Confusion matrix Conjugate gradient method Conjugate transpose Connection form Continuous function Continuum mechanics Control theory Convergent matrix Coordinate change Coordinate system Copositive matrix Coproduct Correlation matrix Covariance and contravariance of vectors Covariance matrix Covariant derivative Coxeter matrix Cramer's rule Critical point (mathematics)Cuthbert Edmund Cullis Cyclic permutation Cyclic subspace DFT matrix Data matrix (multivariate statistics)Defective matrix Definite matrix Definiteness of a matrix Degree matrix Degree of a polynomial Density matrix Descriptive statistics Design matrix Desnanot–Jacobi identity Determinant Diagonal matrix Diagonalizable matrix Diagonally dominant matrix Differentiable function Differential form Differential geometry Dimension Dimension theorem for vector spaces Dimensionality reduction Distance matrix Distributed computation Distributive property Distributivity Division (mathematics)Document-term matrix Dot product Doubly stochastic matrix Douglas West (mathematician)Dover Publications Dual linear program Dual space Duplication and elimination matrices Dutch language Dyadics Eberhard Knobloch Economics Edmonds matrix Eigenbasis Eigendecomposition Eigenvalue Eigenvalue, eigenvector and eigenspace Eigenvalues and eigenvectors Eigenvector Einstein notation Einstein tensor Electromagnetic tensor Electromagnetism Element (mathematics)Elementary matrix Elementary particle Elementary row operations Elizabeth Meckes Ellipse Elliptic partial differential equation Elwin Bruno Christoffel Emily Riehl Emphasis (typography)Empty product Encryption Encyclopedia of Mathematics Endomorphism ring Engineering Equations of motion Equivalence of categories Equivalent matrix Euclidean distance matrix Euclidean geometry Euclidean group Euclidean space European Mathematical Society Even permutation Examples of vector spaces Exchange matrix Extension (predicate logic)Exterior algebra Exterior calculus Exterior covariant derivative Exterior derivative Exterior form Exterior product Fermion Fiber bundle Field (mathematics)Field (physics)Finite element method Finite field Finite graph Finite group Fisher information matrix Flat (geometry)Floating-point arithmetic Fock matrix Force Forward substitution Frobenius matrix Function composition Functional analysis Fundamental matrix (computer vision)Fundamental matrix (linear differential equation)Fuzzy associative matrix Gabriel Cramer Galilean group Gamas's theorem Game theory Gamma matrices Gauge group Gauss Gauss elimination Gaussian elimination Gauss–Jordan elimination Gell-Mann matrices Gene H. Golub General linear group General relativity Generalized inverse Generalized permutation matrix Generator matrix Geodesic Geometric algebra Geometric transformation Geometrical optics Geometry Georg Frobenius George Abram Miller German language Gerolamo Cardano Glossary of linear algebra Glossary of tensor theory Gluon field strength tensor Gordon Royle Gottfried Wilhelm Leibniz Gotthold Eisenstein Graduate Texts in Mathematics Gram matrix Gram–Schmidt process Graph theory Greg Gbur Gregorio Ricci-Curbastro Group (mathematics)Group representation Hadamard matrix Hadamard product (matrices)Hamel basis Hamel dimension Hamiltonian matrix Hankel matrix Harold Edwards (mathematician)Hartree–Fock method Haynsworth inertia additivity formula Henry Bradley Henry F. Baker Hermann Grassmann Hermann Weyl Hermitian form Hermitian matrix Hessenberg matrix Hessian matrix Higher-order singular value decomposition Hilbert matrix Hilbert space Hill cipher Historia Mathematica Hodge star operator Hollow matrix Householder transformation Hurwitz-stable matrix Hyperbola Hypercomplex number Hyperlink Idempotent matrix Identity matrix If and only if Image (mathematics)Imperial College Implicit function theorem Improper rotation Incidence matrix Indefinite matrix Indefinite orthogonal group Independent equation Indeterminate (variable)Index notation Infinitesimal Infinity Initial object Inner product Inner product space Integer matrix Inverse matrix Inverse of a matrix Invertible Invertible matrix Involutory matrix Irregular matrix Isomorphic Isomorphism Jabotinsky matrix Jacobian matrix and determinant James Joseph Sylvester James Murray (lexicographer)Jan Arnoldus Schouten Jan de Witt Japanese mathematics Jean-Bernard Zuber Jean Dieudonné Jean Tirole Jiří Matoušek (mathematician)John B. Conway John Newsome Crossley John Wiley & Sons John von Neumann Jones calculus Jordan normal form Joseph Dauben Joseph Needham Journal of Computational and Applied Mathematics Karl Weierstrass Ken Riley (physicist)Kernel (matrix)Kirchhoff's circuit laws Kronecker delta Kronecker product Kurt Hensel LU decomposition Laplace expansion Laplacian matrix Least squares Lehmer matrix Leibniz formula (determinant)Leibniz formula for determinants Lens (optics)Leon Mirsky Leonard I. Schiff Leonhard Euler Leopold Kronecker Levi-Civita connection Levi-Civita symbol Lie derivative Light wave Limit of a sequence Linda Reichl Linear algebra Linear combination Linear differential equation Linear equation Linear functional Linear independence Linear least squares Linear map Linear operator Linear span Linear subspace Linear system Linear transformation List of matrices List of named matrices Lloyd N. Trefethen Local minimum Logical equivalence Logical matrix Lorentz group Lower-case Lower triangular matrix MIT Press MacTutor History of Mathematics Archive Main diagonal Manifold MapReduce Marcel Dekker Markov chain Mary L. Boas Mass Mathematical Methods in the Physical Sciences Mathematical formulation of quantum mechanics Mathematical objects Mathematician Mathematics Mathematics Magazine Matrix (biology)Matrix (geology)Matrix (printing)Matrix addition Matrix calculus Matrix congruence Matrix consimilarity Matrix decomposition Matrix diagonalization Matrix equivalence Matrix exponential Matrix function Matrix group Matrix inverse Matrix inversion Matrix logarithm Matrix mechanics Matrix multiplication Matrix multiplication algorithm Matrix norm Matrix normal distribution Matrix of ones Matrix product Matrix representation of conic sections Matrix ring Matrix similarity Matrix theory (physics)Matrix unit Max Born Maxime Bôcher McGraw–Hill Measurement in quantum mechanics Metric tensor Metric tensor (general relativity)Metzler matrix Michael Artin Michael Healy (statistician)Minimax theorem Minor (linear algebra)Mixed strategy Mixed tensor Module (mathematics)Molecular orbital Molecules Moment matrix Moment of inertia Monic polynomial Monoidal category Moore matrix Moore–Penrose pseudoinverse Multi-index notation Multilinear algebra Multiplication Multivector Neil Trudinger Network theory Nilpotent matrix Non-commutative Noncommutative ring Nonmetricity tensor Nonnegative matrix Normal matrix Normal mode Normed vector space Null space Null vector Nullity theorem Number Number theory Numerical analysis Numerical linear algebra Numerical stability O'Reilly Media One-form Operation (mathematics)Optical filter Orientation (geometry)Orientation (mathematics)Orthogonal Orthogonal complement Orthogonal group Orthogonal matrices Orthogonal matrix Orthogonal projection Orthogonality Orthonormality Outer product Outline of linear algebra Overcompleteness Overlap matrix Oxford University Press Parallel algorithm Parallelogram Parentheses Partial derivative Partial differential equation Particle accelerator Pascal matrix Pascual Jordan Paul Halmos Paul Wiegmann Pauli matrices Pauline van den Driessche Payoff matrix Penrose graphical notation Pentadiagonal matrix Perfect matrix Permutation matrix Perron–Frobenius theorem Persymmetric matrix Pfaffian Philosophical Transactions of the Royal Society of London Physical system Physics Pick matrix Poincaré group Polar decomposition Polarization (physics)Polynomial Polynomial matrix Polynomial ring Positive-definite matrix Positive definite matrix Precision (statistics)Prentice Hall Principia Mathematica Probabilities Probability distribution Probability vector Projection (linear algebra)Projection matrix Projective geometry Projective linear group Projective space Projective transformation Pseudo-Euclidean space Pseudoinverse Pseudotensor QR decomposition Quadratic form Quadratic programming Quadric Quantum chromodynamics Quantum field theory Quantum mechanics Quark Quaternion Quaternionic matrix Raising and lowering indices Random matrix Random variable Rank (linear algebra)Rank of a matrix Rank–nullity theorem Rational number Ray (geometry)Ray (optics)Ray transfer matrix analysis Real number Recursion Redheffer matrix Reducing subspace Reflection (mathematics)Regular representation Representation theory Ricci calculus Ricci curvature Richard A. Brualdi Riemann curvature tensor Ring (mathematics)Roger Horn Roothaan equations Rotation (mathematics)Rotation matrix Routh–Hurwitz matrix Row and column spaces Row echelon form Row equivalence Row matrix Row operations Rule of Sarrus S-matrix Saddle point Saul Teukolsky Scalar (mathematics)Scalar multiplication Scaling (geometry)Schur complement Schur decomposition Second derivative Seidel adjacency matrix Seifert matrix Seki Kowa Semiring Sequence (mathematics)Serge Lang Sesquilinear form Set (mathematics)Shear mapping Shear matrix Shift matrix Signature matrix Similarity matrix Singular value decomposition Skew-Hermitian matrix Skew-symmetric matrix Skyline matrix Sparse matrix Special linear group Special unitary group Spectral theorem Spectroscopy Spectrum of a matrix Spin group Spin tensor Spinor Springer-Verlag Square bracket Square matrices Square matrix Square root of a matrix Squeeze mapping State-transition matrix Statistics Steven Weinberg Stieltjes matrix Stiffness method Stochastic matrix Strassen algorithm Stress–energy tensor Subgroup Substitution matrix Subtraction Supermatrix Superring Sylvester equation Sylvester matrix Symmetric algebra Symmetric group Symmetric matrix Symmetric tensor Symmetrization Symmetry Symmetry in physics Symplectic matrix Symplectic structure System of linear equations Tensor Tensor (intrinsic definition)Tensor algebra Tensor bundle Tensor calculus Tensor contraction Tensor density Tensor field Tensor operator Tensor product Tensors in curvilinear coordinates Tetrad (index notation)Text mining Tf-idf The American Mathematical Monthly The Nine Chapters on the Mathematical Art Thesaurus Thomas N. E. Greville Thomas W. Hawkins Jr.Toeplitz matrix Topological vector space Torsion tensor Totally positive matrix Totally unimodular matrix Trace (linear algebra)Trace of a matrix Transformation matrix Transport phenomena Transpose Transpose of a linear map Triangular matrix Tridiagonal matrix Truth table Tsit Yuen Lam Tullio Levi-Civita Tutte matrix Two-point tensor Unimodular matrix Unipotent Unit square Unit vector Unitary matrix Universal property University of St Andrews Upper-case Upper bound Upper triangular matrix Van der Waerden notation Vandermonde matrix Variance Vector (mathematics and physics)Vector space Vladimir Arnold Voigt notation Walsh matrix Wang Ling (historian)Weak interaction Website Weighing matrix Werner Heisenberg Weyl tensor Weyr canonical form Wiley-Interscience Wilhelm Jordan (geodesist)William Rowan Hamilton Woldemar Voigt Woodbury matrix identity Wronskian Z-matrix (chemistry)Z-matrix (mathematics)Zero matrix Zero vector space Édouard Brézin Élie Cartan

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