**LA_GEESX** computes for a real/complex square matrix , the
eigenvalues, the real-Schur/complex-Schur form , and, optionally, the
matrix of Schur vectors , where is orthogonal/unitary.
This gives the Schur factorization

Optionally, it also orders the eigenvalues on the diagonal of the Schur form so that selected eigenvalues are at the top left, computes a reciprocal condition number for the average of the selected eigenvalues, and computes a reciprocal condition number for the right invariant subspace corresponding to the selected eigenvalues. The leading columns of form an orthonormal basis for this invariant subspace.

A real matrix is in real-Schur form if it is block upper triangular with and blocks along the main diagonal. blocks are standardized in the form

where . The eigenvalues of such a block are .

A complex matrix is in complex-Schur form if it is upper triangular.