A representation for the Drazin inverse of block matrices with a singular generalized Schur complement

Li, Xiezhang

doi:10.1016/j.amc.2011.02.061

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Cited by 7 publications

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“…To the best of our knowledge, there was no explicit formula for the Drazin inverse of M with arbitrary blocks. However, representations for the Drazin inverse of the block matrices were presented in the literature under some conditions [3][4][5][6][7][8][9][10][11][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improved results on the Drazin inverse of a 2 x 2 block matrix in terms of Banachiewicz-Schur forms

Liu¹,

Yang²

2013

Filomat

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In this paper, we derive a representation for the Drazin inverse of a block matrix M = (A B C D) under the assumptions AA π B = 0, CA π B = 0, AA D BSS π = 0, SS D CWAA D (AW) π = 0 and (AW) π AA D BSS D = 0, where S = D − CA D B is the generalized Schur complement. And the representation can be regarded as an unified form of M D because it covers the case either S is nonsingular or zero. Moreover, some alternative representations for the Drazin inverse are presented. Several situations are analyzed and recent results are generalized.

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Section: Introductionmentioning

confidence: 99%

“…Recently, Castro-González and Martínez-Serrano [13] developed the formula of M D under the conditions ind(S) 1 and W = I + A D BS π CA D is nonsingular. Li [19] developed a representation under certain conditions when S is group invertible.…”

Section: Introductionmentioning

confidence: 99%