Products of similar matrices
type: Item
instance of: scholarly article
title: Products of similar matrices
zbMATH Open document ID: 0841.20045
DOI: 10.1016/0024-3795(94)00057-3
author: Frieder Knüppel
published in: Linear Algebra and its Applications
publication date: 1996-07-16T00:00:00Z
review text: Let \(\text{SL}_n(K)\) and \(\text{GL}_n(K)\) denote the special and the general linear group of dimension \(n\) over \(K\), respectively. Assume \(|K|\geq 2n\). The author shows, if \(\Omega\) is a nontrivial similarity class in \(\text{SL}(V)\), then every element in \(\text{SL}(V)\) is a product of \(n + 2\) or fewer elements in \(\Omega\). Further, assume \(\text{char }K\neq 2\) and \(|K|\geq 7\) and \(n\geq 4\). If \(\Phi\) is a nontrivial conjugacy class of \(\text{GL}_n(K)\), then every element in \(\text{SL}_n(K)\) is a product of at most \(n+4\) elements in \(\Phi\Phi^{-1}\).
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20H20
zbMATH DE Number: 841740
zbMATH Keywords: covering number
zbMATH Keywords: special linear groups
zbMATH Keywords: general linear groups
zbMATH Keywords: similarity classes
zbMATH Keywords: conjugacy classes
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00057-3
OpenAlex ID: W2026196568
cites work: Q3695451
cites work: Decomposition of equiaffinities into reflections
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cites work: Products of cyclic conjugacy classes in the groups \(\text{PSL}(n,F)\)
cites work: A factorization theorem for matrices
cites work: Q4002378
cites work: Similarity of matrices under SL(n,K)
description: scientific article; zbMATH DE number 841740