Introduction

Abstract

A {2}-inverse for a given matrix A is any matrix G satisfying the second of the four conditions defining the unique Moore-Penrose Inverse of A:

$$(1)\;\mathrm{AGA}=\mathrm{A}\;\;\;\;(1.1)$$

$$(2)\;\mathrm{GAG}=\mathrm{G}\;\;\;\;(1.2)$$

$$(3)\;\mathrm{(AG)'}=\mathrm{AG}\;\;\;\;(1.3)$$

$$(4)\;\mathrm{(GA)'}=\mathrm{GA}\;\;\;\;(1.4)$$

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