In the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary complex square matrix as unitarily equivalent to an upper triangular matrix whose diagonal elements are the eigenvalues of the original matrix.
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discipline of linear algebra, the Schurdecomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary...
A\mathbf {x} =\mathbf {b} } , the matrix A can be decomposed via the LU decomposition. The LU decomposition factorizes a matrix into a lower triangular matrix...
{\displaystyle A} . Similarly as for the Schurdecomposition, every square matrix A {\displaystyle A} can be decomposed as A = P − 1 J P {\displaystyle A=P^{-1}JP}...
the Schurdecomposition and for his work on group representations (Schur's lemma). Schur published under the name of both I. Schur, and J. Schur, the...
factorized is a normal or real symmetric matrix, the decomposition is called "spectral decomposition", derived from the spectral theorem. A (nonzero) vector...
A} . When the matrix being decomposed is Hermitian, the spectral decomposition is a special case of the Schurdecomposition (see the proof in case of normal...
algebra, the complete orthogonal decomposition is a matrix decomposition. It is similar to the singular value decomposition, but typically somewhat cheaper...
inversion lemma, which relates the two Schur complements of M: M/D and M/A (see "Derivation from LDU decomposition" in Woodbury matrix identity § Alternative...
of the more general Schurdecomposition which holds for all square matrices. Let A be a square matrix. Then by Schurdecomposition it is unitary similar...
is normal if and only if it is unitarily diagonalizable: By the Schurdecomposition, we have A = U T U*, where U is unitary and T upper-triangular. Since...
value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schurdecomposition. LAPACK...
In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the...
algebra, the tensor rank decomposition or the r a n k − R {\displaystyle rank-R} decomposition of a tensor is the decomposition of a tensor in terms of...
normal form is usually avoided in numerical analysis; the stable Schurdecomposition or pseudospectra are better alternatives. Canonical basis Canonical...
{\displaystyle Z} which are inside the unit circle. Lyapunov equation Schurdecomposition Sylvester equation Chow, Gregory (1975). Analysis and Control of...
stronger properties, but these are sufficient; alternatively the Schurdecomposition can be used, which is less popular but somewhat easier to prove)...
about triangularization, namely, that any square matrix A has a Schurdecomposition. This means that A is unitarily equivalent (i.e. similar, using a...
respectively. Other methods to process data include Schurdecomposition and Cholesky decomposition. In comparison to these, Levinson recursion (particularly...
In linear algebra, a Block LU decomposition is a matrix decomposition of a block matrix into a lower block triangular matrix L and an upper block triangular...
1016/j.laa.2004.10.003. Paige, Chris; Van Loan, Charles (1981), "A Schurdecomposition for Hamiltonian matrices", Linear Algebra and its Applications, 41:...
analysis, the Schur complement method, named after Issai Schur, is the basic and the earliest version of non-overlapping domain decomposition method, also...
open) problems of computing decomposition numbers for general linear groups and symmetric groups are actually equivalent. Schur algebras were used by Friedlander...
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