SEARCH ALL
FACTS & STATISTICS
Advanced view
Search encyclopedia, statistics and forums:
Listed below are some important classes of matrices used in mathematics : For the square matrix section, see square matrix. ...
Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote quotations related to: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ...
(0,1)-matrix or binary matrix - a matrix with all elements either 0 or 1.Adjacency matrix - a (0,1)-matrix that is square with all diagonal elements zero. Used to represent the connectivity of a graph.Alternating sign matrix - a generalization of permutation matrices that arises from Dodgson condensation .Anti-Hermitian matrix - another name for a skew-Hermitian matrix . Anti-symmetric matrix - another name for a skew-symmetric matrix . Band matrix - a square matrix with all entries off a diagonally bordered "band" equal to zero.Bezoutian matrix - a tool for efficient location of polynomial zeros Block diagonal matrix - a block matrix with entries only on the diagonal.Block matrix - a matrix partitioned in sub-matrices called blocks.Cartan matrix Circulant matrix - a matrix where each row is a circular shift of its predecessor.Companion matrix - the companion matrix of a polynomial is a special form of matrix, whose eigenvalues are equal to the roots of the polynomial.Coxeter matrix Diagonal matrix - a square matrix with all entries off the main diagonal equal to zero.Diagonalizable matrix - a square matrix similar to a diagonal matrix. It has a complete set of linearly independent eigenvectors .Distance matrix Gell-Mann matrices Generalized permutation matrix - a square matrix with precisely one nonzero element in each row and column.Gramian matrix - a real symmetric matrix that can be used to test for linear independence of any function .Hadamard matrix - square matrix with entries +1, −1 whose rows are mutually orthogonal.Hankel matrix - a matrix with constant off diagonals; also an upside down Toeplitz matrix. A square Hankel matrix is symmetric.Hermitian matrix - a square matrix which is equal to its conjugate transpose , A = A * . Hessenberg matrix - an "almost" triangular matrix, for example, an upper Hessenberg matrix has zero entries below the first subdiagonal. Hessian matrix Hilbert matrix - a Hankel matrix with elements H ij i + j − 1)−1 . Identity matrix - a square diagonal matrix, with all entries on the main diagonal equal to 1, and the rest 0.Invertible matrix - a square matrix with a multiplicative inverse.Matrix exponential - defined by the exponential seriesMatrix representation of conic sections Nilpotent matrix Nonnegative matrix - a matrix with all nonnegative entries. Normal matrix - a square matrix that commutes with its conjugate transpose . Normal matrices are precisely the matrices to which the spectral theorem applies.Orthogonal matrix - a matrix whose inverse is equal to its transpose , A −1 = A T Orthonormal matrix - matrix whose columns are orthonormal vectors.Overlap matrix Pauli matrices Payoff matrix Permutation matrix - matrix representation of a permutation .Persymmetric matrix - a matrix that is symmetric about its northeast-southwest diagonal, i.e., a ij a n −j +1,n −i +1 Pick matrix - occurs in the study of analytical interpolation problemsPositive-definite matrix - a Hermitian matrix with every eigenvalue positive.Positive matrix - a matrix with all positive entries. S matrix - in physics Singular matrix - a noninvertible square matrix.Similarity matrix Skew-Hermitian matrix - a square matrix which is equal to the negative of its conjugate transpose , A * = −A . Skew-symmetric matrix - a matrix which is equal to the negative of its transpose , A T A . Sparse matrix - containing mostly zerosSquare matrix - an n by n matrix. The set of all square matrices form an associative algebra with identity.Stochastic matrix - a positive matrix describing a stochastic process . The sum of entries of any row is one.Substitution matrix Symmetric matrix - a square matrix which is equal to its transpose , A = A T .Symplectic matrix - a square matrix preserving a standard skew-symmetric form.Toeplitz matrix - a matrix with constant diagonals.Totally positive matrix - a matrix with determinants of all its square submatrices positive. It is used in generating the reference points of Bézier curve in computer graphics . Totally unimodular matrix - a matrix for which every non-singular square submatrix is unimodular . This has some implications in the linear programming relaxation of an integer program .Transformation matrix Transition matrix - a matrix representing the probabilities of changing from one state to anotherTriangular matrix - a matrix with all entries above the main diagonal equal to zero (lower triangular) or with all entries below the main diagonal equal to zero (upper triangular).Tridiagonal matrix - a matrix with the only nonzero entries on the main diagonal and the diagonals just above and below the main one.Unimodular matrix - a square matrix with determinant +1 or −1.Unitary matrix - a square matrix whose inverse is equal to its conjugate transpose , A −1 = A * .Vandermonde matrix - a row consists of 1, a , a 2 , a 3 , etc., and each row uses a different variableWalsh matrix Wronskian Zero matrix - a matrix with all entries equal to zero.
Feeds |
Contact