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

This paper studies the concept of stable perturbation Bn× n for the core-EP inverse of a matrix An× 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 ∥ Bπ-Aπ∥ 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.