Representation for the generalized Drazin inverse of block matrices in Banach algebras

Mosić, Dijana; Djordjević, Dragan S.

doi:10.1016/j.amc.2012.06.008

Cited by 11 publications

(7 citation statements)

References 15 publications

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“…In Section 3, we give representations for N d under weaker restrictions and generalize some results of [3]. Furthermore, in Section 4, considering some matrix decompositions, we apply N d to get some new expressions for the Drazin inverse of a 2 × 2 block matrix under some conditions, which extend several results of [8,[16][17][18] and recover some result of [4,19] for the case of Drazin inverses. Throughout this paper, denote by I the identity matrix of proper size, write A π for I − AA d , and let…”

Section: Introductionmentioning

confidence: 71%

The Drazin inverse of the sum of four matrices and its applications

Zhang

Mosić

Guo

2018

Linear and Multilinear Algebra

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Our aim is to establish relations between Drazin inverses of the pesudo-block matrix (P, Q, R, S ) and the block matrix P R S Q , where R 2 = S 2 = 0. Based on the relations, we give representations for Drazin inverses of the sum P + Q + R + S under weaker restrictions. As its applications, several expressions for Drazin inverses of a 2 × 2 block matrix are presented under some assumptions. Our results generalize several results in the literature.

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Section: Introductionmentioning

confidence: 71%

The Drazin inverse of the sum of four matrices and its applications

Zhang

Mosić

Guo

2018

Linear and Multilinear Algebra

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“…By elementary computations, we can check the following result which was proved for Banach algebra elements in [10].…”

Section: Introductionmentioning

confidence: 94%

Characterizations of the Image-Kernel (p, q)-Inverses

Mosić

2015

Bull. Malays. Math. Sci. Soc.

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“…In recent years, the representations of the Drazin inverse for matrices or operators have been investigated (see [1,4,5,7,9]). The Drazin inverse of an operator or a matrix has various applications in singular differential equations and singular difference equations, Markov chains, and iterative methods [2].…”

Section: Introductionmentioning

confidence: 99%