decomposition into triangular matrices

См. также в других словарях:

• 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

• 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

• 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

• 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

• Singular value decomposition — Visualization of the SVD of a 2 dimensional, real shearing matrix M. First, we see the unit disc in blue together with the two canonical unit vectors. We then see the action of M, which distorts the disk to an ellipse. The SVD decomposes M into… …   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

• 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

• Determinant — This article is about determinants in mathematics. For determinants in epidemiology, see Risk factor. In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific… …   Wikipedia

• List of numerical analysis topics — This is a list of numerical analysis topics, by Wikipedia page. Contents 1 General 2 Error 3 Elementary and special functions 4 Numerical linear algebra …   Wikipedia