Perturbations of the eigenprojections of a factorized Hermitian matrix

We give the perturbation bounds for the eigenprojections of a Hermitian 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 relative gaps between the eigenvalues and may thus be much less pessimistic than the standard norm estimates.