Permutation-like matrix groups
type: Item
instance of: scholarly article
title: Permutation-like matrix groups
zbMATH Open document ID: 1134.15010
author: Grega Cigler
published in: Linear Algebra and its Applications
publication date: 2007-04-10T00:00:00Z
review text: Let \(\mathcal{G}\subset \mathbb{C}^{n\times n}\) be a finite group of matrices. If every \(X\in\mathcal{G}\) is similar to a permutation matrix, then \(\mathcal{G}\) is called a permutation-like group. The author investigates if a permutation-like group is equivalent to a group of permutation matrices. He finds counterexamples, but he has an affirmative answer under certain conditions, in particular for \(n=3\) and \(5\).
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 20G20
zbMATH DE Number: 5141629
zbMATH Keywords: permutation matrices
zbMATH Keywords: groups of matrices
zbMATH Keywords: matrix similarity
zbMATH Keywords: counterexamples
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
full work available at URL: j.laa.2006.11.007
OpenAlex ID: W1982915583
cites work: Irreducible semigroups of matrices with eigenvalue one
cites work: Q4317890
DOI: 10.1016/J.LAA.2006.11.007
description: scientific article; zbMATH DE number 5141629