### The n-Inverses of a Matrix

#### Abstract

The concept of a left n-inverse of a bounded linear operator on a complex Banach space was

introduced recently. Previously, there have been results on products and tensor products of left

n-inverses, and the representation of left n-inverses as the sum of left inverses and nilpotent

operators was being discussed. In this paper, we give a spectral characterization of the left

n-inverses of a nite (square) matrix. We also show that a left n-inverse of a matrix T is the

sum of the inverse of T and two nilpotent matrices.

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