Alternative algebraic perturbation expressions for the $m$-weak group inverse and $m$-weak core inverse

Abstract

This paper presents several novel algebraic perturbation formulas for the $m$-weak group inverse and the $m$-weak core inverse of a matrix $A$. The nonsingular matrix utilized in these formulas is contingent upon a basis for the nullspace of $(A^{k})^{*}$, where $k$ denotes the index of the matrix $A$. In particular, some new algebraic perturbation formulas for the Drazin inverse and core-EP inverse are presented for a special case.