Error bounds for a general perturbation of the Drazin inverse

摘要

The paper solves a long standing problem of finding error bounds for a general perturbation of the Drazin inverse. The bounds are given in terms of the distance between the matrices together with the distance between their eigenprojections. Estimates using the gap between subspaces are also given. Recent results of several authors, including Castro, Koliha, Straškraba (Soochov J. Math., to appear) Wang and Wei (Linear Algebra Appl. 258 (1997) 179–186) can be recovered as special cases of our theorems.