In this paper a representation is given for the Drazin inverse of a 2 × 2 operator matrix, extending to Banach spaces results of Hartwig, Li and Wei [SIAM J. Matrix Anal. Appl., 27 (2006) pp. 757–771]. Also, formulae are derived for the Drazin inverse of an operator matrix M under some new conditions.

In this note the representations of the Drazin inverse of a 2×2 block matrix M = [ A B C D ] , where A and D are square matrices, have been recently developed under some assumptions. We derive formulae for the Drazin inverse of a block matrix M under conditions weaker than those in the papers [9], [11], [12] and [14]. 2000 Mathematics Subject Classification: 15A09

In this paper a representation is given for the Drazin inverse of a 2 × 2 operator matrix, extending to Banach spaces results of Hartwig, Li and Wei [SIAM J. Matrix Anal. Appl., 27 (2006) pp. 757–771]. Also, formulae are derived for the Drazin inverse of an operator matrix M under some new conditions.

Block representations of the Drazin inverse of a bipartite matrix A = 2 4 0 B C 0 3 5 in terms of the Drazin inverse of the smaller order block product BC or CB are presented. Relationships between the index of A and the index of BC are determined, and examples are given to illustrate all such possible relationships.

We study semi-iterative methods for an approximate solution of a linear equation x = Tx+c with a bounded linear operator T acting on a Banach space X, considering separately the cases when λ = 1 is an isolated and accumulation spectral point for T . We give necessary and sufficient conditions for the convergence of a semi-iterative method, utilizing the generalized Drazin inverse introduced by ...

In this paper we investigate the continuity of the Drazin inverse of a bounded linear operator on Banach space. Then as a corollary, among other things, we get the well known result of Campbell and Meyer ([1]) for the continuity of the Drazin inverse of square matrix.

We propose a finite algorithm for computing Drazin inverse of two-variable polynomial matrices based on Greville s finite algorithm for computing Drazin inverse of a constant matrix. Also a three-dimensional recursive algorithm to do that is deduced. Examples show that these methods are feasible and the implementation is developed in the symbolic package MATLAB. 2002 Elsevier Inc. All rights re...