lower-upper triangular decomposition

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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

• LU decomposition — In linear algebra, LU decomposition (also called LU factorization) is a matrix decomposition which writes a matrix as the product of a lower triangular matrix and an upper triangular matrix. The product sometimes includes a permutation matrix as… …   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

• Crout matrix decomposition — In linear algebra, the Crout matrix decomposition is an LU decomposition which decomposes a matrix into a lower triangular matrix (L), an upper triangular matrix (U) and, although not always needed, a permutation matrix (P). The Crout matrix… …   Wikipedia

• QR decomposition — In linear algebra, the QR decomposition (also called the QR factorization) of a matrix is a decomposition of the matrix into an orthogonal and a right triangular matrix. The QR decomposition is often used to solve the linear least squares problem …   Wikipedia

• Lie group decomposition — In mathematics, Lie group decompositions are used to analyse the structure of Lie groups and associated objects, by showing how they are built up out of subgroups. They are essential technical tools in the representation theory of Lie groups and… …   Wikipedia

• Bruhat decomposition — In mathematics, the Bruhat decomposition G = BWB into cells can be regarded as a general expression of the principle of Gauss–Jordan elimination, which generically writes a matrix as a product of an upper triangular and lower triangular matrices… …   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

• Cholesky decomposition — In linear algebra, the Cholesky decomposition or Cholesky triangle is a decomposition of a Hermitian, positive definite matrix into the product of a lower triangular matrix and its conjugate transpose. It was discovered by André Louis Cholesky… …   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

• Orthogonal matrix — In linear algebra, an orthogonal matrix (less commonly called orthonormal matrix[1]), is a square matrix with real entries whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors). Equivalently, a matrix Q is orthogonal if… …   Wikipedia