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Spectral study of {R, s+1, k}- and {R, s+1, k, *}-potent matrices

Author:
Catral, M.  Lebtahi, L.  Stuart, J.  Thome, N.  


Journal:
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS


Issue Date:
2020


Abstract(summary):

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. (C) 2019 Elsevier B.V. All rights reserved.


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