Decomposition of matrices into commutators of involutions
type: Item
instance of: scholarly article
title: Decomposition of matrices into commutators of involutions
zbMATH Open document ID: 1004.20026
DOI: 10.1016/S0024-3795(01)00597-3
author: Baodong Zheng
published in: Linear Algebra and its Applications
publication date: 2002-08-28T00:00:00Z
review text: Let \(\text{SL}_nF\) be the special linear group over some field \(F\). An element \(T\) in \(\text{SL}_nF\) is called an involution if \(T^2=1\). A matrix \(A\) in \(\text{SL}_nF\) is called a commutator of involutions if there are two involutions \(S\) and \(T\) in \(\text{SL}_nF\) such that \(A=TST^{-1}S^{-1}\). The author shows: If \(F\) is the complex number field or the real number field, then every matrix \(A\) in \(\text{SL}_nF\) is either a commutator of involutions or it can be written as a product of two commutators of involutions. Not every element \(A\) is a commutator of involutions.
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 1790221
zbMATH Keywords: involutions
zbMATH Keywords: commutators
zbMATH Keywords: special linear groups
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
cites work: Commutators in the Special and General Linear Groups
cites work: The elements of the orthogonal group \(\Omega_ n(V)\) as products of commutators of symmetries
cites work: Q4719990
cites work: Products of involutions
cites work: Product of two involutions
cites work: SL(V) is 4-reflectional
cites work: A factorization theorem for matrices
description: scientific article; zbMATH DE number 1790221