Drazin Inverse Of Block Matrix Research Articles

Explicit formulae for the generalized drazin inverse of block matrices over a Banach algebra

In this paper, we give expressions for the generalized Drazin inverse of a (2,2,0) block matrix over a Banach algebra under certain circumstances, utilizing which we derive the generalized Drazin inverse of a 2x2 block matrix in a Banach algebra under weaker restrictions. Our results generalize and unify several results in the literature.

On additive properties of the Drazin inverse of block matrices and representations

In this paper, we give a new additive formula for the Drazin inverse under conditions weaker than those used in some current literature on this subject. Also, we obtain representations for the Drazin inverse of a complex block matrix having generalized Schur complement equal to zero.

A note on computational formulas for the Drazin inverse of certain block matrices

In this paper, we give a computational formula for the Drazin inverse of the sum P+Q, then applying it we give some computational formulas for the Drazin inverse of block matrix (A and D are square) with generalized Schur complement S=D−CA D B is nonsingular under some conditions. These results extend the results about the Drazin inverse of M given by R. Hartwig, X. Li and Y. Wei (SIAM J. Matrix Anal. Appl. 27:757–771, 2006) and by C. Deng (J. Math. Anal. Appl. 368:1–8, 2010).

Explicit representations of the Drazin inverse of block matrix and modified matrix

A new result on the Drazin inverse of 2 × 2 block matrix , where A and C are square matrices are presented, extended in the case when D = 0, the well-known representation for the Drazin inverse of M, given by Hartwig, Meyer and Rose in 1977, respectively. Using that new result, an explicit representation for the Drazin inverse of a modified matrix P + RS and its generalized matrix PQ + RS are also presented.

Expressions for the drazin inverse of a 2×2 Block Matrix

The Drazin inverse of a 2×2 block matrix is considered. Expressions for the Drazin inverse of block matrix M in terms of the individual blocks A B C, and D are delivered under some conditions. These results partially answer the question by Campbell in 1983.