Orthogonal tripotent matrices

TL;DR

This paper characterizes tripotent orthogonal matrices using various matrix equations, properties, and invariants, providing new insights into their structure and properties.

Contribution

It introduces multiple characterizations of tripotent orthogonal matrices, expanding understanding of their algebraic and spectral properties.

Findings

Characterizations via matrix equations and powers

Properties related to rank and trace

Relationships involving A, A^*, and A^{}

Abstract

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.