On g-inverses of a bordered matrix: revisited Original Research Article

In this article we study the structure and properties of g-inverse M− of the bordered matrix image which is partitioned conforming with M, image by applying the multiple quotient singular value decomposition QQ-SVD. From the structure of M−, we discuss the relations among D1,D2,D3 and D4, and derive equivalent conditions for M− to be a bordered matrix. By studying D1 in M−, we obtain some equivalent conditions for D1 to be a g-inverse of A.