Representations of the weighted WG inverse and a rank equation's solution

The core-EP and BT inverses for rectangular matrices were studied recently in the literature.The main aim of this paper is to unify both concepts by means of a new kind of generalized inverse called W -weighted q-BT inverse. We analyze its existence and uniqueness by considering an adequate matrix system. Basic properties and some interesting characterizations are proved for this new weighted generalized inverse. Also, we give a canonical form of the W -weighted q-BT inverse by means of the weighted core-EP decomposition.

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“…Let X := A ⋄q ,W . By Definition 2.4 and Theorem 2.11 (ii) it is clear that X satisfies both conditions in (9).…”

Section: Algebraic Characterizationsmentioning

confidence: 95%

“…Uniqueness. Let X be an arbitrary matrix satisfying both conditions in (9). Since R((W AW P (AW ) q ) † ) = R(P (AW ) q (W AW ) * ), the second condition in (9) implies X = (W AW P (AW ) q ) † Z for some matrix Z.…”

Section: Algebraic Characterizationsmentioning

confidence: 99%

The W -weighted BT inverse

Ferreyra

Thome

Torigino

2022

Quaestiones Mathematicae

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“…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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“…The set of all weighted generalized Drazin inverse of matrix A is denoted by A{GD, W }. We further refer interested readers to [9], [11], [24], and [28] for more works on generalized inverses and their extensions.…”

mentioning

confidence: 99%

W-weighted GDMP inverse for rectangular matrices

Kumar

Shekhar

Mishra

2022

ELA

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In this article, we introduce two new generalized inverses for rectangular matrices called $W$-weighted generalized-Drazin--Moore--Penrose (GDMP) and $W$-weighted generalized-Drazin-reflexive (GDR) inverses. The first generalized inverse can be seen as a generalization of the recently introduced GDMP inverse for a square matrix to a rectangular matrix. The second class of generalized inverse contains the class of the first generalized inverse. We then exploit their various properties and establish that the proposed generalized inverses coincide with different well-known generalized inverses under certain assumptions. We also obtain a representation of $W$-weighted GDMP inverse employing EP-core nilpotent decomposition. We define the dual of $W$-weighted GDMP inverse and obtain analogue results. Further, we discuss additive properties, reverse- and forward-order laws for GD, $W$-weighted GD, GDMP, and $W$-weighted GDMP generalized inverses.

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Representations of the weighted WG inverse and a rank equation's solution

Cited by 4 publications

References 29 publications

The W -weighted BT inverse

The W -weighted BT inverse

Generalized group elements and their orders

W-weighted GDMP inverse for rectangular matrices

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