Decomposition of matrices into 2-involutions
type: Item
instance of: scholarly article
title: Decomposition of matrices into 2-involutions
zbMATH Open document ID: 0773.15005
DOI: 10.1016/0024-3795(93)90294-X
author: Hong You
author: Jizu Lan
published in: Linear Algebra and its Applications
publication date: 1993-10-25T00:00:00Z
review text: Consider the group \(SL_ nF\) of all \(n\) by \(n\) matrices with determinant 1 over a field \(F\). Let \(\text{res }A\) denote \(\text{rank }(A-I)\) for any \(A\) in \(SL_ nF\). A matrix \(A\) is called a \(k\)-involution if \(A^ 2=I\) and \(\text{res} A=k\). The authors prove that every matrix \(A\) in \(SL_ nF\) is the product of at most \([(\text{res} A+1)/2]+2\) 2-involutions for \(n\geq 3\) if \(\text{Char} F\neq 2\) and for \(n\geq 4\) if \(\text{Char} F=2\). Here \([r]\) denotes the integer part of the rational number \(r\). An example shows that the number \([(\text{res} A+1)/2]+2\) cannot be reduced in some cases.
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 205213
zbMATH Keywords: decomposition
zbMATH Keywords: factorization
zbMATH Keywords: involution
reviewed by: Joseph A. Ball
MaRDI profile type: Publication
cites work: Products of central collineations
cites work: Q3228640
cites work: Products of reflections in the general linear group over a division ring
cites work: Decomposition of matrices into simple involutions
cites work: The operator factorization problems
cites work: Q4712686
cites work: Q4723951
Wikidata QID: Q127109526
description: scientific article; zbMATH DE number 205213