Search results for "K-involutory"
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Matrices A such that A^{s+1}R = RA* with R^k = I
2018
[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.
Spectral study of {R, s + 1, k}- and {R, s + 1, k, *}-potent matrices
2020
[EN] The {R, s +1, k}- and {R, s +1, k, *}-potent matrices have been studied in several recent papers. We continue these investigations from a spectral point of view. Specifically, a spectral study of {R, s + 1, k} -potent matrices is developed using characterizations involving an associated matrix pencil (A, R). The corresponding spectral study for {R, s+ 1, k, *}-potent matrices involves the pencil (A*, R). In order to present some properties, the relevance of the projector I - AA(#). where A(#) is the group inverse of A is highlighted. In addition, some applications and numerical examples are given, particularly involving Pauli matrices and the quaternions.