Theory and applications of matrix perturbations, with respect to Hankel matrices and power formulae
Robert E. Hartwig · International Journal of Systems Science · 1979
Recurrence relations are used to obtain formulae for the powers of additive and order perturbations of a square matrix A. These formulae are related to such concepts as controllability and may be applied to compute the perturbed power nulspaces and the perturbed principal idempotents associated with the zero eigenvalue. It is shown how rank-one and row-column perturbations are, to a large extent, determined by their Hankel sequences which are defined in terms of the Drazin inverse of A and the perturbations in question.