Expressing infinite matrices as products of involutions

Roksana Słowik

doi:10.1016/j.laa.2012.07.032

Expressing infinite matrices as products of involutions

Roksana Słowik

Department of Mathematics (RMS/RMS1)

Research output: Contribution to journal › Article › peer-review

27 Citations (Scopus)

Abstract

We take into consideration ± ^UT∞(K) - the group of upper triangular infinite matrices whose entries lying on the main diagonal are equal to either 1 or -1. We show that for any field K, every element of this group can be expressed as a product of at most five involutions. Moreover, we prove that if K is a field of characteristic different from 2, then four involutions suffice.

Original language	English
Pages (from-to)	399-404
Number of pages	6
Journal	Linear Algebra and Its Applications
Volume	438
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2012.07.032
Publication status	Published - 1 Jan 2013

Keywords

Infinite matrices
Products of involutions
Triangular matrices

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2012.07.032

Cite this

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AB - We take into consideration ± UT∞(K) - the group of upper triangular infinite matrices whose entries lying on the main diagonal are equal to either 1 or -1. We show that for any field K, every element of this group can be expressed as a product of at most five involutions. Moreover, we prove that if K is a field of characteristic different from 2, then four involutions suffice.

KW - Infinite matrices

KW - Products of involutions

KW - Triangular matrices

UR - https://www.scopus.com/pages/publications/84869082355

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DO - 10.1016/j.laa.2012.07.032

M3 - Article

AN - SCOPUS:84869082355

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SP - 399

EP - 404

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1

ER -

Expressing infinite matrices as products of involutions

Abstract

Keywords

ASJC Scopus subject areas

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