Additive results for the Drazin inverse of block matrices and applications

Additive results for the Drazin inverse of block matrices and applications

In this paper we consider the Drazin inverse of a sum of two matrices and we derive additive formulas under conditions weaker than those used in some recent papers on the subject. Like a corollary we get the main results from the paper of H. Yang, X. Liu (The Drazin inverse of the sum of two matrices and its applications, Journ.Comp.Appl.Math., 235 (2011) 1412–1417). As an application we give s...

Generalized Drazin inverse of certain block matrices in Banach algebras

Several representations of the generalized Drazin inverse of an anti-triangular block matrix in Banach algebra are given in terms of the generalized Banachiewicz--Schur form.  

Ela Representations for the Drazin Inverse of Block Cyclic Matrices

REPRESENTATIONS FOR THE DRAZIN INVERSE OF BLOCK CYCLIC MATRICES M. CATRAL AND P. VAN DEN DRIESSCHE Abstract. A formula for the Drazin inverse of a block k-cyclic (k ≥ 2) matrix A with nonzeros only in blocks Ai,i+1, for i = 1, . . . , k (mod k) is presented in terms of the Drazin inverse of a smaller order product of the nonzero blocks of A, namely Bi = Ai,i+1 · · ·Ai−1,i for some i. Bounds on ...

Representations for the Drazin inverse of block cyclic matrices

Some additive results on Drazin inverse

Some additive perturbation results for Drazin inverses are given. In particular, a formula is given for the Drazin inverse of a sum of two matrices, when one of the products of these matrices vanishes. Some special applications of this are also considered. © 2001 Elsevier Science Inc. All rights reserved. AMS classification: 15A09; 15A23