On Orthogonalization in the Inverse Power Method

When the inverse power method is used to compute eigenvectors of asymmetric matrix corresponding to close eigenvalues, the computed
eigenvectors may not be orthogonal. The cure for the problem is to
orthogonalize the vectors using the Gram--Schmidt algorithm. In this note
it is shown that the orthogonalization process does not cause the quality
of the eigenvectors to deteriorate.
Also cross-referenced as UMIACS-TR-99-64