On g-inverses of a bordered matrix: revisited

Abstract

In this article we study the structure and properties of g-inverse M − of the bordered matrix M= A B C 0 , which is partitioned conforming with M, M −= D 1 D 2 D 3 D 4 by applying the multiple quotient singular value decomposition QQ-SVD. From the structure of M −, we discuss the relations among D 1, D 2, D 3 and D 4, and derive equivalent conditions for M − to be a bordered matrix. By studying D 1 in M −, we obtain some equivalent conditions for D 1 to be a g-inverse of A.