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block-triangular matrix

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  • Triangular matrix — In the mathematical discipline of linear algebra, a triangular matrix is a special kind of square matrix where the entries either below or above the main diagonal are zero. Because matrix equations with triangular matrices are easier to solve… …   Wikipedia

  • Block LU decomposition — In linear algebra, a Block LU decomposition is a decomposition of a block matrix into a lower block triangular matrix L and an upper block triangular matrix U . This decomposition is used in numerical analysis to reduce the complexity of the… …   Wikipedia

  • Matrix decomposition — In the mathematical discipline of linear algebra, a matrix decomposition is a factorization of a matrix into some canonical form. There are many different matrix decompositions; each finds use among a particular class of problems. Contents 1… …   Wikipedia

  • Block reflector — A block reflector is an orthogonal, symmetric matrix that reverses a subspace whose dimension may be greater than one. * see abstract here http://locus.siam.org/SINUM/volume 25/art 0725014.htmlIt is built out of many elementary reflectors.It is… …   Wikipedia

  • Matrix (mathematics) — Specific elements of a matrix are often denoted by a variable with two subscripts. For instance, a2,1 represents the element at the second row and first column of a matrix A. In mathematics, a matrix (plural matrices, or less commonly matrixes)… …   Wikipedia

  • Matrix exponential — In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group.… …   Wikipedia

  • Jordan matrix — In the mathematical discipline of matrix theory, a Jordan block over a ring R (whose identities are the zero 0 and one 1) is a matrix which is composed of 0 elements everywhere except for the diagonal, which is filled with a fixed element… …   Wikipedia

  • Band matrix — In mathematics, particularly matrix theory, a band matrix is a sparse matrix whose non zero entries are confined to a diagonal band, comprising the main diagonal and zero or more diagonals on either side. Contents 1 Matrix bandwidth 2… …   Wikipedia

  • Positive-definite matrix — In linear algebra, a positive definite matrix is a matrix that in many ways is analogous to a positive real number. The notion is closely related to a positive definite symmetric bilinear form (or a sesquilinear form in the complex case). The… …   Wikipedia

  • Diagonalizable matrix — In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P such that P −1AP is a diagonal matrix. If V is a finite dimensional vector space, then a linear …   Wikipedia

  • Nilpotent matrix — In linear algebra, a nilpotent matrix is a square matrix N such that for some positive integer k. The smallest such k is sometimes called the degree of N. More generally, a nilpotent transformation is a linear transformation L of a vector space… …   Wikipedia

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