m-weak group inverses in a ring with involution

Zhou, Yukun; Chen, Jianlong; Zhou, Mengmeng

doi:10.1007/s13398-020-00932-1

Cited by 19 publications

(9 citation statements)

References 22 publications

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“…In [13] the authors extended the notion of the WG inverse to rectangular matrices. In [28], Zhou et al proposed the m-weak group in ring with involution and gave some characterizations of it. For A ∈ C n×n a matrix of index k, the m-weak group inverse is the unique matrix A w ○ m = X ∈ C n×n satisfying the equations…”

Section: Notations and Terminologymentioning

confidence: 99%

The $m$-weak core inverse

Ferreyra¹,

Malik²

2023

Preprint

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Since the day the core inverse has been known in a paper of Bakasarly and Trenkler, it has been widely researched. So far, there are four generalizations of this inverse for the case of matrices of an arbitrary index, namely, the BT inverse, the DMP inverse, the core-EP inverse and the WC inverse. In this paper we introduce a new type of generalized inverse for a matrix of arbitrary index to be called m-weak core inverse which generalizes the core-EP inverse, the WC inverse, and therefore the core inverse. We study several properties and characterizations of the m-weak core inverse by using matrix decompositions.

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Section: Notations and Terminologymentioning

confidence: 99%

The $m$-weak core inverse

Ferreyra¹,

Malik²

2023

Preprint

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“…Lemma 2.6. [4,18] Let a ∈ R. If there exist x ∈ R and k ∈ Z + such that xa k+1 = a k and ax 2 = x, then…”

Section: Preliminariesmentioning

confidence: 99%

“…Lemma 2.10. [18] Let a ∈ R. Then x is a weak group inverse of a if and only if there exist x ∈ R and k ∈ Z + such that…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Weak group inverses and partial isometries in proper *-rings

Zhou

Chen

Zhou

et al. 2021

Linear and Multilinear Algebra

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A weak group element is introduced in a proper * -ring. Several equivalent conditions of weak group elements are investigated. We prove that an element is pseudo core invertible if it is both partial isometry and weak group invertible. Reverse order law and additive property of the weak group inverse are presented. Finally, under certain assumption on a, equivalent conditions of a W a * = a * a W are presented by using the normality of the group invertible part of an element in its group-EP decomposition.

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“…en, Ferryra et al [9] extended the definition of WG inverse to the general matrix, defined the weighted WG inverse, and gave its expression, properties, and characterizations; Mosić and Zhang [10] established the weighted WG inverse of Hilbert space operator; Zhou et al [11] generalized WG inverse to a proper * -ring and gave a new characterization of WG inverse; Zhou et al [12] generalized m-WG inverse to a unitary ring with involution and gave some properties of m-WG inverse; Mosić and Stanimirović [13] gave new characterizations, limit representations, integral representations, and perturbation formulae of the WG inverse.…”

Section: Introductionmentioning

confidence: 99%