0000000000357995

AUTHOR

M. Catral

showing 2 related works from this author

On a matrix group constructed from an {R,s+1,k}-potent matrix

2014

Let R is an element of C-nxn be a {k}-involutory matrix (that is, R-k = I-n) for some integer k >= 2, and let s be a nonnegative integer. A matrix A is an element of C-nxn is called an {R,s + 1, k}-potent matrix if A satisfies RA = A(s+1)R. In this paper, a matrix group corresponding to a fixed {R,s + 1, k}-potent matrix is explicitly constructed, and properties of this group are derived and investigated. This group is then reconciled with the classical matrix group G(A) that is associated with a generalized group invertible matrix A.

Group inverseMatrix groupÀlgebra lineal{R s+1 k}-potent matrixMATEMATICA APLICADAMatrius (Matemàtica)
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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.

S-potent matrixSpectrumMatrius (Matemàtica){R s+1 k}-potent matrixMATEMATICA APLICADAK-involutory matrix
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