The core-EP inverse: a numerical approach for its acute perturbation
Mengmeng Zhou, Jianlong Chen, Néstor Thome · Linear and Multilinear Algebra · 2024
This paper studies the concept of stable perturbation B∈Cn×n for the core-EP inverse of a matrix A∈Cn×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 Bπ 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.