 
Summary: Linear Algebra and its Applications 430 (2009) 16
Available online at www.sciencedirect.com
www.elsevier.com/locate/laa
Generators of matrix algebras in dimension 2 and 3
Helmer Aslaksen a,
, Arne B. Sletsjøe b
a Department of Mathematics, National University of Singapore, Singapore 117543, Singapore
b Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway
Received 14 June 1995; accepted 8 May 2006
Available online 8 October 2008
Submitted by T.J. Laffey
Abstract
Let K be an algebraically closed field of characteristic zero and consider a set of 2 × 2 or 3 × 3 matrices.
Using a theorem of Shemesh, we give conditions for when the matrices in the set generate the full matrix
algebra.
© 2008 Published by Elsevier Inc.
Keywords: Generator; Matrix; Algebra
1. Introduction
Let K be an algebraically closed field of characteristic zero, and let Mn = Mn(K) be the
algebra of n × n matrices over K. Given a set S = {A1, . . . , Ap} of n × n matrices, we would
