ON RELATIVE RESIDUAL BOUNDS FOR THE EIGENVALUES OF A HERMITIAN MATRIX

Let H be a Hermitian matrix, X an orthonormal matrix, and M = XHX. Th en the eigenvalues of M approximate some eigenvalues of H with an abso lute error bounded by \\HX - XM\\(2). The main interest in this work i s the relative distance between the eigenvalues of M and some part of the spectrum of H. It is shown that distance depends on the angle betw een the ranges of X and HX.