Further results on the representation of the Drazin inverse of a 2 x 2 block matrix

The aim of this paper is to establish an explicit representation of the Drazin inverse of a 2 x 2 block matrix M = [GRAPHICS] , where A and D are square matrices, in terms of the Drazin inverses of A and D. First, we give a formula for the Drazin inverse of M with the blocks satisfying the conditions BC = 0. BDC = 0, and BD2 = 0. Further, we derive representations of the Drazin inverse of M under less restrictive conditions than those found in the current literature. (C) 2009 Elsevier Inc. All rights reserved.