GDMP-inverses of a matrix and their duals

Hernández, M. V.; Lattanzi, Marina; Thome, Néstor

doi:10.1080/03081087.2020.1857678

Cited by 8 publications

(2 citation statements)

References 25 publications

(27 reference statements)

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“…As well as for 1D inverses, it is easy to verify that the DMP inverse, GDMP inverse [11], and D1 inverse all are different in general. We recall that a matrix X ∈ C n×n is called a G-Drazin of A ∈ C n×n if AXA = A and A k X = XA k .…”

Section: D Inverse and D1 Inverse Of Square Matricesmentioning

confidence: 99%

1D inverse and D1 inverse of square matrices

Sahoo,

Maharana,

Sitha

et al. 2024

MMN

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In this paper we introduce two new classes of inverses for square matrices, which are called 1Drazin (in short, 1D) inverse and Drazin1 (in short, D1) inverse. Next, we investigated the existence and uniqueness of 1D inverse and its dual D1 inverse. Some representation and characterizations of these inverses are derived. In addition to this, we obtain some properties of 1D and D1 inverses through idempotent and binary relations.

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Section: D Inverse and D1 Inverse Of Square Matricesmentioning

confidence: 99%

1D inverse and D1 inverse of square matrices

Sahoo,

Maharana,

Sitha

et al. 2024

MMN

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“…In 2020, Hernández et al [13] introduced another generalized inverse called generalized-Drazin-Moore-Penrose (GDMP) inverse. The definition of GDMP inverse is stated next.…”

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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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