See 'dgees.f' for all details.
DGEES computes for an N-by-N real non-symmetric matrix A, the
eigenvalues, the real Schur form T, and, optionally, the matrix of
Schur vectors Q. This gives the Schur factorization A = Q*T*(Q**T).
Optionally, it also orders the eigenvalues on the diagonal of the
real Schur form so that selected eigenvalues are at the top left.
The leading columns of Q then form an orthonormal basis for the
invariant subspace corresponding to the selected eigenvalues.
A matrix is in real Schur form if it is upper quasi-triangular with
1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the
form
[ a b ]
[ c a ]
where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).