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Matrices A such that A^{s+1}R = RA* with R^k = I

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Matrices A such that A^{s+1}R = RA* with R^k = I

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Catral, Minerva; Lebtahi, Leila; Stuart, Jeffrey; Thome, Néstor

Aquest document és un/a article, creat/da en: 2018

We study matrices A in C^{nxn} such that A^(s+1)R = RA* where R^k = I_n, and s, k are nonnegative integers with k >= 2; such matrices are called {R,s + 1,k; *}-potent matrices. The s = 0 case corresponds to matrices such that A = RA*R^(-1) with R^k = In, and is studied using spectral properties of the matrix R. For s >= 1, various characterizations of the class of {R,s + 1,k, *}-potent matrices and relationships between these matrices and other classes of matrices are presented.

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