arXiv subjects

Kezheng Zuo

Publications and source records attributed to Kezheng Zuo.

9 recordsLinked to original sources

arXiv2026

Dual orthogonal tripotent matrices

In this paper, we study dual orthogonal tripotent matrices, defined by $\hat{A}^3=\hat{A} = \hat{A}^*$, and examine their fundamental algebraic properties. Additionally, we establish several characterizations of this class of matrices using matrix averages involving $\hat{A}$, $\hat{A}_e$, $\hat{A}^*$, $\hat{A}\sp{\scriptscriptstyle N}$, as well as integer powers of products such as $\hat{A}\hat{A}^*$ and $\hat{A}^*\hat{A}$. These results enrich the theory of dual generalized matrix classes and reveal new perspectives on related dual quaternion matrices.

math.RA↗

arXiv2026

Further results for the dual Hartwig-Spindelb{ö}ck decomposition and its applications

In this paper, we introduce two new forms of the dual Hartwig-Spindelb{ö}ck decomposition and employ them to derive explicit representations for several classes of dual generalized inverses. Building on these representations, we further explore and characterize the relationships and properties of these inverses, investigate the dual composite generalized inverses, and verify the applicability of dual partial orders. The proposed decomposition provides a systematic and convenient framework for the study of dual matrices.

math.RA↗

arXiv2025

Orthogonal tripotent matrices

In this paper, we present different characterizations of tripotent orthogonal matrices (i.e., A^3 = A = A^* ) in terms of matrix equations, integer powers of AA^* and A^*A, average of A, A^*, and A^{\dagger}, rank of matrices, and trace of matrices. We study certain properties of this class of matrices.

math.RA↗

arXiv2025

The Bott-Duffin drazin inverse and its application

The paper introduce a new type of generalized inverse, called Bott-Duffin drazin inverse (or, in short, BDD-inverse) of a complex square matrix, and give some of its properties, characterizations and representations. Furthermore, We discuss the problem of the minimum P-norm solution of the constraint matrix equation by using the Bott-Duffin drazin inverse, and give Cramer s rule for this minimum P-norm solution.

math.RA↗

arXiv2025

Further properties and representations of the W-weighted m-weak group inverse

The purpose of this paper is to explore more properties and representations of the W-weighted m-weak group (in short, W-m-WG) inverse. We first explore an interesting relation between two projectors with respect to the W-m-WG inverse. Then, the W-m-WG inverse is represented by various generalized inverses including W-weighted Drazin inverse, W-weighted weak group inverse, W-weighted core inverse, etc. We also give three concise explicit expressions for the W-m-WG inverse. Moreover, a canonical form of the W-m-WG inverse is presented in terms of the singular value decomposition. Finally, several numerical examples are designed to illustrate some results given in the paper.

math.RA↗

arXiv2024

The W-weighted m-weak group MP inverse and its applications

We extend the concept of the m-weak group MP inverse of a square matrix to a rectangular matrix, called the W-weighted m-weak group MP inverse, which also unifies the W-weighted weak core inverse and W-weighted DMP inverse. Some properties, characterizations and representations of this new generalized inverse are shown. Additionally, applications of the W-weighted weak group MP inverse are given in solving a constrained optimization problem and a class of consistent matrix equations.

math.FA↗

arXiv2023

The m-DMP inverse in Minkowski space and its applications

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 the m-DMP inverse in solving a system of linear equations and a constrained optimization problem.

math.OC↗

arXiv2023

Further characterizations and representations of the Minkowski inverse in Minkowski space

This paper is aimed to identify some new characterizations and representations of the Minkowski inverse in Minkowski space. First of all, a few representations of {1,3m}, {1,2,3m}, {1,4m} and {1,2,4m}-inverses are given in order to represent the Minkowski inverse. Secondly, some famous characterizations of the Moore-Penrose inverse are extended to that of the Minkowski inverse. Thirdly, 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.

math.FA↗

arXiv2020

A new generalized inverse of matrices from core-EP decomposition

A new generalized inverse for a square matrix $H\in\mathbb{C}^{n\times n}$, called CCE-inverse, is established by the core-EP decomposition and Moore-Penrose inverse $H^†$. We propose some characterizations of the CCE-inverse. Furthermore, two canonical forms of the CCE-inverse are presented. At last, we introduce the definitions of CCE-matrices and $k$-CCE matrices, and prove that CCE-matrices are the same as $i$-EP matrices studied by Wang and Liu in [The weak group matrix, Aequationes Mathematicae, 93(6): 1261-1273, 2019].

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