Algebraic Perturbation Theorems of Core Inverse A㊮ and Core-EP Inverse A㊯ - Xingping Sheng (Journal of Mathematics)
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.