Decomposition of matrices into commutators of reflections.
type: Item
instance of: scholarly article
title: Decomposition of matrices into commutators of reflections.
zbMATH Open document ID: 1035.15014
author: Hong You
published in: Journal of Systems Science and Complexity
publication date: 2003-01-01T00:00:00Z
review text: It is proved that every \(n\times n\)-matrix \(A\) belonging to the group \(\text{GL}_n(F)\) defined over field \(F\) is the product of at most \([\operatorname {res} A/2]+2\) commutators of reflections [see \textit{E. Cartan} (1938), \textit{J. Dieudonne} (1948) and \textit{P. Scherk}, Proc. Am. Math. Soc. 1, 481--491 (1950; Zbl 0039.01004)] for all \(n\geq 2\), except for \(n=2\) and \(F=F_2\), where \([\;]\) denotes the integer part of a rational number and \(\operatorname {res}A= \text{rank}(A-I)\).
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 20H20
zbMATH DE Number: 1917030
zbMATH Keywords: generators of \(\text{SL}_n(F)\) group
zbMATH Keywords: decomposition of \(n\times n\)-matrices
zbMATH Keywords: commutators of reflections
reviewed by: A. A. Bogush
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1917030