SchurDecomposition

SchurDecomposition[m]

yields the Schur decomposition for a numerical matrix m, given as 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.

Details and Options

The original matrix m is equal to q.t.Conjugate[Transpose[q]]. »
The matrix m must be square.
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, and 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]]. »
For real-valued matrices m, setting the option RealBlockDiagonalForm->False allows complex values on the diagonal of the t matrix.