On the perturbation of singular analytic matrix functions: A generalization of Langer and Najman's results
Fernando De Terán · Operators and Matrices · 2011
Given a singular n n matrix function A( ) , analytic in a neighborhood of an eigenvalue 0 C , and perturbations, B( ,) , such that B( ,0) 0 and analytic in and near ( 0 ,0) , we provide sufficient conditions on these perturbations for the existence of eigenvalue expansions of the perturbed matrix A( ) + B( ,) near 0 . We also describe the first order term of these expansions. This extends to the singular case some results by Langer and Najman.