arXiv subjects

Tan Mei

Publications and source records attributed to Tan Mei.

3 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{\"o}ck decomposition and its applications

In this paper, we introduce two new forms of the dual Hartwig-Spindelb{\"o}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↗