Algebraic Perturbation Theorems of Core Inverse A ㊮ and Core-EP Inverse A ㊯

Abstract

In this paper, the algebraic perturbation theorems of the core inverse A ㊮ and core-EP inverse A ㊯ are discussed for a square singular matrix A with different indices, and the expressions of the algebraic perturbation for these two new generalized inverses are presented. As their applications, some properties of the core inverse A ㊮ and core-EP inverse A ㊯ are proven again by using the expressions of their algebraic perturbation. In the last section, two numerical examples are considered to demonstrate the main results.