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Groups of Matrices That Act Monopotently

Authors :
Leo Livshits
Joshua D. Hews
Source :
The Electronic Journal of Linear Algebra. 32:423-437
Publication Year :
2017
Publisher :
University of Wyoming Libraries, 2017.

Abstract

In the present article, the authors continue the line of inquiry started by Cigler and Jerman, who studied the separation of eigenvalues of a matrix under an action of a matrix group. The authors consider groups \Fam{G} of matrices of the form $\left[\small{\begin{smallmatrix} G & 0\\ 0& z \end{smallmatrix}}\right]$, where $z$ is a complex number, and the matrices $G$ form an irreducible subgroup of $\GL(\C)$. When \Fam{G} is not essentially finite, the authors prove that for each invertible $A$ the set $\Fam{G}A$ contains a matrix with more than one eigenvalue. The authors also consider groups $\Fam{G}$ of matrices of the form $\left[\small{\begin{smallmatrix} G & x\\ 0& 1 \end{smallmatrix}}\right]$, where the matrices $G$ comprise a bounded irreducible subgroup of $\GL(\C)$. When \Fam{G} is not finite, the authors prove that for each invertible $A$ the set $\Fam{G}A$ contains a matrix with more than one eigenvalue.

Details

ISSN :
10813810
Volume :
32
Database :
OpenAIRE
Journal :
The Electronic Journal of Linear Algebra
Accession number :
edsair.doi...........9711c04a4605bf445010b2326397e9b3
Full Text :
https://doi.org/10.13001/1081-3810.3479