The Drazin inverses of sum and difference of idempotents

Deng, Chun Yuan

doi:10.1016/j.laa.2008.10.017

Cited by 41 publications

(24 citation statements)

References 18 publications

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“…Recently, some formulas for the Drazin inverse of a sum of two matrices (or two bounded operators in a Banach space) under some conditions were given (see [4,5,7,8,9,10,11,14] and references therein). Let us remark that the group inverse…”

Section: Introduction Throughout This Paper Cmentioning

confidence: 99%

On the group inverse of linear combinations of two group invertible matrices

Liu¹,

Wu²,

Benítez

2011

ELA

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Section: Introduction Throughout This Paper Cmentioning

confidence: 99%

On the group inverse of linear combinations of two group invertible matrices

Liu¹,

Wu²,

Benítez

2011

ELA

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“…Again, it was extended for morphisms on arbitrary additive categories by Chen et al in [8]. More results on the Drazin inverse or the generalized Drazin inverse can also be found in [3,5,6,8,9,11,12,15]. In particular we must cite [13]: in this paper, the authors, under the commutative condition of AB = BA (when A and B are Drazin invertible linear operators in Banach spaces), gave explicit representations of (A + B) D in term of A, A D , B, and B D .…”

Section: §1 Introduction and Previous Resultsmentioning

confidence: 99%

Some additive results on Drazin inverse

Liu

Qin

Benítez

2015

Appl. Math. J. Chin. Univ.

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Abstract. In this paper, we investigate additive results of the Drazin inverse of elements in a ring R. Under the condition ab = ba, we show that a + b is Drazin invertible if and only ifis Drazin invertible, where the superscript D means the Drazin inverse. Furthermore we find an expression of (a + b) D . As an application we give some new representations for the Drazin inverse of a 2 × 2 block matrix.

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“…In 2011, Yang and Liu [10] gave the result of (P + Q) D when P Q 2 = 0 and P QP = 0, and in 2012, Bu et al [12] gave the representation of (P + Q) D when P 2 Q = 0, Q 2 P = 0 and P 3 Q = 0, QP Q = 0, QP 2 Q = 0 respectively. Other results have been studied in [4,[13][14][15][16][17][18]19].…”

Section: Introductionmentioning

confidence: 99%