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

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 ( Aᵏ )*, 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.