The m-WG inverse in Minkowski space

Hui, Wu; Wang, Hongxing; Jin, Hongwei

doi:10.2298/fil2204125w

Filomat

2022

DOI: 10.2298/fil2204125w

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The m-WG inverse in Minkowski space

Wu Hui

Hongxing Wang

Hongwei Jin

Abstract: In this paper, we introduce them-WG inverse in Minkowski space. Firstly, we show the existence and the uniqueness of the m-WG inverse. Secondly, we give representations of the m-WG inverse. Thirdly, we characterize the m-WG inverse by applying a bordered matrix. In addition, we extend the generalized Cayley-Hamilton theorem to the m-WG inverse matrix. Finally, we apply the m-WG inverse to solve linear equations in Minkowski space.

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Cited by 3 publications

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The 𝔪-WG° inverse in the Minkowski space

Liu,

Zhang,

Jin

2023

Open Mathematics

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In this article, we study the m {\mathfrak{m}} -WG ∘ {}^{\circ } inverse which presents a generalization of the m {\mathfrak{m}} -WG inverse in the Minkowski space. We first show the existence and the uniqueness of the generalized inverse. Then, we discuss several properties and characterizations of the m {\mathfrak{m}} -WG ∘ {}^{\circ } inverse by using the core-EP decomposition. Applying the generalized inverse, we obtain the solutions of some matrix equations in Minkowski space.

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The 𝔪-WG° inverse in the Minkowski space

Liu,

Zhang,

Jin

2023

Open Mathematics

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The m-DMP inverse in Minkowski space and its applications

Gao,

Zuo,

Wang

2024

Filomat

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This paper first introduces a new generalized inverse in Minkowski space, called the m-DMP inverse, and discusses its algebraic and geometrical properties. The second objective is to characterize the m-DMP inverse equivalently by ranges, null spaces and matrix equations, and show its integral and limiting representations and several explicit expressions. Finally, the paper gives applications of them-DMP inverse in solving a system of linear equations and a constrained optimization problem.

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Further characterizations and representations of the Minkowski inverse in Minkowski space

Gao

Zuo

Wang

et al. 2023

MATH

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<abstract><p>This paper serves to identify some new characterizations and representations of the Minkowski inverse in Minkowski space. First of all, a few representations of $ \{1, 3^{\mathfrak{m}}\} $-, $ \{1, 2, 3^{\mathfrak{m}}\} $-, $ \{1, 4^{\mathfrak{m}}\} $- and $ \{1, 2, 4^{\mathfrak{m}}\} $-inverses are given in order to represent the Minkowski inverse. Second, some famous characterizations of the Moore-Penrose inverse are extended to that of the Minkowski inverse. Third, using the Hartwig-Spindelböck decomposition, we present a representation of the Minkowski inverse. And, based on this result, an interesting characterization of the Minkowski inverse is showed by a rank equation. Finally, we obtain several new representations of the Minkowski inverse in a more general form, by which the Minkowski inverse of a class of block matrices is given.</p></abstract>

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The m-WG inverse in Minkowski space

Cited by 3 publications

References 20 publications

The 𝔪-WG° inverse in the Minkowski space

The 𝔪-WG° inverse in the Minkowski space

The m-DMP inverse in Minkowski space and its applications

Further characterizations and representations of the Minkowski inverse in Minkowski space

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