SchurDecomposition

SchurDecomposition[m] yields the Schur decomposition for a numerical matrix m. The result is a list q, t where q is an orthonormal matrix and t is a block upper triangular matrix.

SchurDecomposition[m, a] gives the generalized Schur decomposition of m with respect to a.

The original matrix m is equal to q . t . Conjugate[Transpose[q]].

SchurDecomposition[m, Pivoting -> True] yields a list q, t, d where d is a permuted diagonal matrix such that m . d is equal to d . q . t . Conjugate[Transpose[q]].

SchurDecomposition[m, a] yields a list of matrices q, s, p, t where q and p are orthonormal matrices, s and t are upper triangular matrices, such that m is given by q . s . Conjugate[Transpose[p]] and a is given by q . t . Conjugate[Transpose[p]].

See Section 3.7.10.

Implementation Notes: see Section A.9.4.

See also: QRDecomposition, LUDecomposition, SingularValueDecomposition, JordanDecomposition.

New in Version 2; modified in 5.0.

Further Examples