Dual orthogonal tripotent matrices

Abstract

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