I've come across an irregularity when extracting the eigenvectors when using
the CISS method to solve the eigenvalue problem. I'm solving a generalized
hermitian problem, and it looks like the resulting eigenvectors are
M-orthogonalized with each other (the M-inner products of different
eigenvectors are approximately 0, as expected), but are normalized using the
L2-inner product, not the M-inner product. Basically, the matrix V'*M*V (V
being a matrix composed of the extracted eigenvectors) is diagonal, but the
diagonals are much larger than 1, and the matrix V'*V has non-zero diagonals,
but the diagonal elements are exactly equal to 1.
This only happens if I use the CISS method. If I use the Arnoldi method for
example, the eigenvectors are normalized as expected. Is there any particular
reason for this, or is this an error in the implementation?