The group inverse of a companion matrix

Puystjens, Roland; Hartwig, Robert E.

doi:10.1080/03081089708818521

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Cited by 46 publications

(31 citation statements)

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“…In our development, we extend the following characterization of the Drazin index given by Puystjens and Hartwig [10]: given a regular element a ∈ R, then ind(a) ≤ 1 if and only if ind(a + 1 − aa − ) = 0, for one and hence all choices of a − ∈ a{1}.…”

Section: Introductionmentioning

confidence: 99%

Generalized Inverses of a Sum in Rings

Castro‐González

Araújo

Patrício

2010

Bull. Aust. Math. Soc.

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Section: Introductionmentioning

confidence: 99%

Generalized Inverses of a Sum in Rings

Castro‐González

Araújo

Patrício

2010

Bull. Aust. Math. Soc.

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“…The Puystjens-Hartwig Theorem [9] characterizes the group invertibility of a regular element in terms of units. We may rewrite it as the equivalences (1) ⇔ (2) ⇔ (4) in the proposition below.…”

Section: Resultsmentioning

confidence: 99%

On the Drazin index of regular elements

Patrício

Costa

2009

Open Mathematics

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Abstract:It is known that the existence of the group inverse # of a ring element is equivalent to the invertibility of 2 − + 1 − − , independently of the choice of the von Neumann inverse − of . In this paper, we relate the Drazin index of to the Drazin index of 2 − + 1 − − . We give an alternative characterization when considering matrices over an algebraically closed field. We close with some questions and remarks. MSC:15A09, 16A14, 16A30

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“…However, research on the generalized inverses of matrices over non-commutative rings is relatively sparse; see [2], [4], [14], [15]. The purpose of this paper is to study the group inverses of matrices over an important associative ring -a Bezout domain, and generalize some results which are well known and given at present.…”

Section: Introductionmentioning

confidence: 99%

Group inverses for matrices over a Bezout domain

Cao¹,

Li²

2009

ELA

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Abstract. Suppose R is a Bezout domain. In this paper, some necessary and sufficient conditions for the existence of the group inverse for square matrix over R are given, the conditions for the existence of the group inverse of products of matrices are studied, and the equivalent conditions for reverse order law of group inverse of product of matrices are obtained. Also the existence and the representation of the group inverse for a class 2 × 2 block matrices over R are studied, and some well known relative results are generalized.

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The group inverse of a companion matrix

Cited by 46 publications

References 4 publications

Generalized Inverses of a Sum in Rings

Generalized Inverses of a Sum in Rings

On the Drazin index of regular elements

Group inverses for matrices over a Bezout domain

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