The core-EP inverse: a numerical approach for its acute perturbation

Abstract

This paper studies the concept of stable perturbation B ∈ C n × n for the core-EP inverse of a matrix A ∈ C n × n with index k. For a given stable perturbation B of A, explicit expressions of its core-EP inverse B ◯ $ † $ and its projection at zero B π are presented. Then, the perturbation bounds of ∥ B ◯ $ † $ − A ◯ $ † $ ∥ / ∥ A ◯ $ † $ ∥ and ∥ B π − A π ∥ are given provided that B is a stable perturbation of A. In addition, we investigate the concept of acute perturbation of A. We give a perturbation analysis with respect to core-EP inverses. We provide a condition under which the acute perturbation coincides with the stable perturbation for core-EP inverses.