Matrices \(A\) such that \(A^{s+1}R\) = \(RA^\ast\) with \(R^k = I\). (English) Zbl 1391.15044
Summary: We study matrices \(A \in \mathbb{C}^{n \times n}\) such that \(A^{s + 1} R = R A^\ast\) where \(R^k = I_n\), and \(s, k\) are nonnegative integers with \(k \geq 2\); such matrices are called \(\{R, s + 1, k, \ast \}\)-potent matrices. The \(s = 0\) case corresponds to matrices such that \(A = R A^\ast R^{- 1}\) with \(R^k = I_n\), and is studied using spectral properties of the matrix \(R\). For \(s \geq 1\), various characterizations of the class of \(\{R, s + 1, k, \ast \}\)-potent matrices and relationships between these matrices and other classes of matrices are presented.
MSC:
| 15A21 | Canonical forms, reductions, classification |
| 15A09 | Theory of matrix inversion and generalized inverses |
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