PERTURBATIONS OF THE EIGENPROJECTIONS OF A FACTORIZED HERMITIAN MATRIX

We give the perturbation bounds for the eigenprojections of a Hermitia n matrix H = GJG, where G has full column rank and J is nonsingular, under the perturbations of the factor G. Our bounds hold, for example, when G is given with elementwise relative error. Our bounds contain r elative gaps between the eigenvalues and may thus be much less pessimi stic than the standard norm estimates.