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20 pages, 316 KB

Open AccessArticle

The

m

-CCE Inverse in Minkowski Space and Its Applications

by Xin Tan and Xiaoji Liu

Axioms 2025, 14(6), 413; https://doi.org/10.3390/axioms14060413 - 28 May 2025

Viewed by 373

Abstract

In this paper, we introduce a new generalized inverse called

m

-CCE inverse which presents a generalization of the CCE inverse in Minkowski space by using the

m

-core-EP decomposition and the Minkowski inverse. We first show the existence and the uniqueness of [...] Read more.

In this paper, we introduce a new generalized inverse called

m

-CCE inverse which presents a generalization of the CCE inverse in Minkowski space by using the

m

-core-EP decomposition and the Minkowski inverse. We first show the existence and the uniqueness of the generalized inverse. Then, a number of basic properties and diverse characterizations are derived for the

m

-CCE inverse as well as its limit and integral expressions. Additionally, applications of the

m

-CCE inverse are given in solving a system of linear equations. Applying the generalized inverse, we introduce a binary relation based on the

m

-CCE inverse. Full article

(This article belongs to the Special Issue Advances in Linear Algebra with Applications, 2nd Edition)

12 pages, 260 KB

Open AccessArticle

Existence Criteria and Related Relation of the gMP Inverse of Matrices

by Sanzhang Xu, Honglin Zou and Kezheng Zuo

Mathematics 2024, 12(13), 1972; https://doi.org/10.3390/math12131972 - 25 Jun 2024

Viewed by 1224

Abstract

New characterizations of the gMP inverse are provided by the core part of the core-EP decomposition. We also answer the question as to whether X is the gMP inverse of A under the conditions of [...] Read more.

New characterizations of the gMP inverse are provided by the core part of the core-EP decomposition. We also answer the question as to whether X is the gMP inverse of A under the conditions of

R (X) \subseteq R (A^{*} A^{k})

N ({(A^{k})}^{*}) \subseteq N (X)

. We investigate the relationship between the core-EP inverse and the gMP inverse.Using the gMP inverse, the gMP relation is investigated in view of the core-EP decomposition. Full article

11 pages, 292 KB

Open AccessArticle

Two New Matrix Classes Related to the CMP Inverse: CMP and Co-CMP Matrices

by Yinlan Chen, Jiale Gao and Kezheng Zuo

Mathematics 2023, 11(17), 3692; https://doi.org/10.3390/math11173692 - 28 Aug 2023

Cited by 1 | Viewed by 1311

Abstract

This paper focuses on two new matrix classes related to the CMP inverse of a square matrix, called the CMP and co-CMP matrices. Some of their characterizations are identified based on the core-EP decomposition and subspace operations. And, we show an equivalence relationship between the co-CMP matrix set and the intersection of the core matrix set and the co-EP matrix set. The nonsingularity of other matrices closely associated with the co-CMP matrices is considered, and their inverses are presented in a decomposition form. Full article

(This article belongs to the Section A: Algebra and Logic)

11 pages, 252 KB

Open AccessArticle

Core-EP Monotonicity Characterizations for Property-n Matrices

by Jin Zhong and Lin Lin

Mathematics 2023, 11(11), 2531; https://doi.org/10.3390/math11112531 - 31 May 2023

Viewed by 1271

Abstract

A square matrix is said to have property n if there exists a positive integer w such that

A^{w}

is nonnegative. In this paper, we study the core-EP monotonicity for property-n matrices. Some necessary and sufficient conditions for a property-n [...] Read more.

A square matrix is said to have property n if there exists a positive integer w such that

A^{w}

is nonnegative. In this paper, we study the core-EP monotonicity for property-n matrices. Some necessary and sufficient conditions for a property-n matrix to be core-EP monotone are given. Moreover, a necessary and sufficient condition for a real square matrix to have a nonnegative core-EP inverse is also presented. Full article

(This article belongs to the Section E: Applied Mathematics)

11 pages, 316 KB

Open AccessArticle

Two Generalizations of the Core Inverse in Rings with Some Applications

by San-Zhang Xu, Julio Benítez, Ya-Qian Wang and Dijana Mosić

Mathematics 2023, 11(8), 1822; https://doi.org/10.3390/math11081822 - 12 Apr 2023

Cited by 1 | Viewed by 1533

Abstract

In this paper, we introduce two new generalized core inverses, namely, the

(p, q, m)

-core inverse and the

⟨ p, q, n ⟩

-core inverse; both extend the inverses of the

⟨ i, m ⟩

[...] Read more.

In this paper, we introduce two new generalized core inverses, namely, the

(p, q, m)

-core inverse and the

⟨ p, q, n ⟩

-core inverse; both extend the inverses of the

⟨ i, m ⟩

-core inverse, the

(j, m)

-core inverse, the core inverse, the core-EP inverse and the

DMP

-inverse. Full article

(This article belongs to the Special Issue Modeling, Analysis and Optimization for Mathematical Finance, Economics and Risks)

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