Block representations for the Drazin inverse of anti-triangular matrices

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

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.  

A note on the representations for the Drazin inverse of 2 × 2 block matrices

In 1979, Campbell and Meyer proposed the problem of finding a formula for the Drazin inverse of a 2 × 2 matrix M = [ A B C D ] in terms of its various blocks, where the blocks A and D are required to be square matrices. Special cases of the problems have been studied. In particular, a representation of the Drazin inverse of M , denoted by MD , has recently been obtained under the assumptions th...

Some Representations for the Generalized Drazin Inverse of Block Matrices in Banach Algebras

We give explicit representations of the generalized Drazin inverse of a block matrix having generalized Schur complement generalized Drazin invertible in Banach algebras. Also we give equivalent conditions under which the group inverse of a block matrix exists and a formula for its computation. The provided results extend earlier works given in the literature. 2010 Mathematics Subject Classific...