On relative residual bounds for the eigenvalues of a Hermitian matrix Original Research Article

Let H be a Hermitian matrix, X an orthonormal matrix, and M = X*HX. Then the eigenvalues of M approximate some eigenvalues of H with an absolute error bounded by double vertical barHX − XMdouble vertical bar2. The main interest in this work is 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 between the ranges of X and HX.