When is the Hermitian/skew-Hermitian part of a matrix a potent matrix?

Abstract

This paper deals with the Hermitian H(A) and skew-Hermitian part S(A) of a complex matrix A. We characterize all complex matrices A such that H(A), respectively S(A), is a potent matrix. Two approaches are used: characterizations of idempotent and tripotent Hermitian matrices of the form, and a singular value decomposition of A. In addition, a relation between the potency of H(A), respectively S(A), and the normality of A is also studied.