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arXiv · 2607.11900

Dual orthogonal tripotent matrices

Tan Mei·Kezheng Zuo·Yang Si
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Abstract

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.

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Tan Mei, Kezheng Zuo, Yang Si. 2026-06-22. Dual orthogonal tripotent matrices. https://arxiv.org/abs/2607.11900

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