Representations of the Drazin inverse for a class of block 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...

Ela Block Representations of the Drazin Inverse of A

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.