Vol. 13, No. 6, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
An improved bound for the lengths of matrix algebras

Yaroslav Shitov

Vol. 13 (2019), No. 6, 1501–1507
DOI: 10.2140/ant.2019.13.1501
Abstract

Let S be a set of n × n matrices over a field F. We show that the F-linear span of the words in S of length at most

2nlog2n + 4n

is the full F-algebra generated by S. This improves on the n2 3 + 2 3 bound by Paz (1984) and an O(n32) bound of Pappacena (1997).

Keywords
matrix theory, finite-dimensional algebras, generating sets
Mathematical Subject Classification 2010
Primary: 15A03
Secondary: 15A30
Milestones
Received: 14 November 2018
Revised: 6 March 2019
Accepted: 14 May 2019
Published: 18 August 2019
Authors
Yaroslav Shitov
Moscow
Russia