Continuity of the core-EP inverse and its applications

TL;DR

This paper investigates the continuity and perturbation bounds of the core-EP inverse, providing theoretical results, numerical comparisons, and applications to semistable matrices.

Contribution

It introduces new methods to analyze the continuity and perturbation bounds of the core-EP inverse, extending existing results and applying them to semistable matrices.

Findings

Established continuity conditions for the core-EP inverse.

Derived perturbation bounds under specific conditions.

Applied results to semistable matrices.

Abstract

In this paper, firstly we study the continuity of the core-EP inverse without explicit error bounds by virtue of two methods. One is the rank equality, followed from the classical generalized inverse. The other one is matrix decomposition. The continuity of the core inverse can be derived as a particular case. Secondly, we study perturbation bounds for the core-EP inverse under prescribed conditions. Perturbation bounds for the core inverse can be derived as a particular case. Also, as corollaries, the sufficient (and necessary) conditions for the continuity of the core-EP inverse are obtained. Thirdly, a numerical example is illustrated to compare the derived upper bounds. Finally, an application to semistable matrices is provided.