Products of commutators of dilatations
type: Item
instance of: scholarly article
title: Products of commutators of dilatations
zbMATH Open document ID: 0933.15020
DOI: 10.1016/S0024-3795(98)10222-7
author: Hong You
author: Chen Sheng
published in: Linear Algebra and its Applications
publication date: 2000-03-21T00:00:00Z
review text: Let \(SL_nF\) denote the group of all \(n\times n\) matrices with determinant 1 over a field \(F\). Let \(\text{res }A\) denote \(\text{rank}(A-I)\) for \(A\in GL_nF\). A matrix \(A\in GL_nF\) is called a dilation if \(A\) is similar to a matrix \(I_{n-1} \oplus a\) (\(a\neq 1\)). In this paper, it is proved that if \(|F|>4\), then every matrix \(A\in SL_nF\) is the product of at most \([\text{res }A/2]+1\) commutators of dilatations for \(n\geq 2\) ([\ ] denotes the integer part of a rational number).
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 1331315
zbMATH Keywords: commutator
zbMATH Keywords: dilatation
zbMATH Keywords: factorization of matrices
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1331315