Bulletin of the Australian Mathematical Society

Research Article

ON THE LENGTHS OF PAIRS OF COMPLEX MATRICES OF SIZE SIX

M. S. LAMBROUa1 and W. E. LONGSTAFFa2 c1

a1 Department of Mathematics, University of Crete, Iraklion, Crete, Greece (email: lambrou@math.uoc.gr)

a2 School of Mathematics & Statistics, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia (email: longstaf@maths.uwa.edu.au)

Abstract

The length of every pair {A,B} of 6×6 complex matrices is shown to be at most 10, that is, the words in A,B of length at most 10, including the empty word, span the unital algebra generated by A,B. This supports the conjecture that the length of every pair of n×n complex matrices is at most 2n−2, known to be true for n<6.

(Received September 11 2008)

2000 Mathematics subject classification

  • primary 15A30; secondary 47L05

Keywords and phrases

  • length;
  • words

Correspondence:

c1 For correspondence; e-mail: longstaf@maths.uwa.edu.au