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

[EN] We study matrices A is an element of C-n x n 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 = I-n, 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. (C) 2018 Elsevier Inc. All rights reserved.
The second and fourth authors have been partially supported by Ministerio de Economia y Competitividad of Spain (Grant MTM2013-43678-P and Red de Excelencia Grant MTM2017-90682-REDT).