Characterizations and perturbation analysis of a class of matrices related to core-EP inverses

Zhou, Mengmeng; Chen, Jianlong; Thome, Néstor

doi:10.1016/j.cam.2021.113496

Cited by 11 publications

(4 citation statements)

References 32 publications

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“…Consequently, for A ∈ B(H) # , the core-EP (or *core-EP) inverse of A coincides with the core (or dual core) inverse [1]. Significant results about the core and core-EP inverse are established in [2,5,6,9,11,[21][22][23].…”

Section: Ts (Ormentioning

confidence: 92%

Inner-gMP and gMP-inner inverses

STOJANOVİC,

MOSİC

2024

Hacettepe Journal of Mathematics and Statistics

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Solving some systems of operator equations, new kinds of generalized inverses are introduced. Since these new inverses can be expressed by inner and gMP inverses, they are called inner-gMP and gMP-inner inverses. In this way, the concepts of gMP, 1MP and MP1 inverses are generalized. Various representations and characterizations of inner-gMP and gMP-inner inverses are presented. Using the inner and *gMP inverse, we define the inner-*gMP and *gMP-inner inverses which are new extensions of 1MP, MP1 and *gMP inverses. We apply inner-gMP and gMP-inner inverses as well as inner-*gMP and *gMP-inner inverses to solve several kinds of linear equations. Consequently, we obtain solvability of the normal equation which is connected to the least--squares solution. Numerical examples are given to illustrate our results.

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Section: Ts (Ormentioning

confidence: 92%

Inner-gMP and gMP-inner inverses

STOJANOVİC,

MOSİC

2024

Hacettepe Journal of Mathematics and Statistics

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“…In [26], Zou et al extend the notion of weak group inverse from complex matrices to elements in a ring with proper involution. We refer the reader for weak group inverse in [5,6,9,17,21,28,29].…”

Section: Huanyin Chen and Marjan Sheibani *mentioning

confidence: 99%

Generalized group inverse in Banach *-algebras

Chen,

Sheibani

2023

Preprint

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In this paper, we introduce the notion of the generalized group inverse in a *-Banach algebra. This is a natural generalization of weak group inverse for a complex matrix and bounded linear operator over a Hilbert space. We present polar-like property for the generalized group inverse and characterize it by the generalized Drazin inverse. Furthermore, the relations between generalized group inverse and generalized core-EP inverse are investigated. 2020 Mathematics Subject Classification. 15A09, 16U90, 46H05.

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“…Evidently, generalized and weak group elements coincide with each other for a complex matrix. The properties of weak group matrices are thereby extended to the general setting (see [23,27]…”

Section: Generalized Group Elements and Their Ordersmentioning

confidence: 99%

“…If such x exists, it is unique, and denote it by a W ❖ . We refer the reader for weak group inverse in [8,9,12,18,19,20,22,23,26,27,28].…”

Section: Introductionmentioning

confidence: 99%

Generalized group elements and their orders

Chen,

Sheibani

2023

Preprint

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In this paper, we present reverse order of generalized group inverse in a proper Banach algebra. We characterize generalized group elements and determine when an element and its generalized group inverse commute each other. The properties of the generalized group orders are investigated. As applications, new properties of the core-EP order of two complex matrices and Hilbert space operators are thereby extended to wider cases. 2020 Mathematics Subject Classification. 15A09, 16U99, 46H05.

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Characterizations and perturbation analysis of a class of matrices related to core-EP inverses

Cited by 11 publications

References 32 publications

Inner-gMP and gMP-inner inverses

Inner-gMP and gMP-inner inverses

Generalized group inverse in Banach *-algebras

Generalized group elements and their orders

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