Perturbation theory for the eigenvalues of factorised symmetric matrices Original Research Article

We obtain eigenvalue perturbation results for a factorised Hermitian matrix H=GJG* where J2=I and G has full row rank and is perturbed into G+δG, where δG is small with respect to G. This complements the earlier results on the easier case of G with full column rank. Applied to square factors G our results help to identify the so-called quasidefinite matrices as a natural class on which the relative perturbation theory for the eigensolution can be formulated in a way completely analogous to the one already known for positive definite matrices.