Relations between \(\{ K; s+1\} \)-potent matrices and different classes of complex matrices
The authors consider \(\{ K; s+1 \}\)-potent matrices. A matrix \(A \in \mathbb C^{n \times n}\) is called \(\{ K; s+1 \}\)-potent when \(K\,A^{s+1}\,K = A\) where \(K\) is an involutory matrix and \(s \in \{ 1,2,3,\dots \}\). Specifically, \(\{ K; s+1 \}\)-potent matrices are analyzed considering their relations to different classes of complex matrices; these classes of matrices are: \(\{ s+1 \}\)-generalized projectors, \(\{ K \}\)-Hermitian matrices, normal matrices, and matrices \(B \in \mathbb C^{n \times n}\) (anti-)commuting with \(K\) or such that \(K\,B\) is involutory, Hermitian or normal. In addition, some new relations for \(K\)-generalized centrosymmetric matrices are derived.
scientific article; zbMATH DE number 6142071
scientific article