On the lengths of irreducible pairs of complex matrices
Authors:
W. E. Longstaff and Peter Rosenthal
Journal:
Proc. Amer. Math. Soc. 139 (2011), 37693777
MSC (2010):
Primary 15A30; Secondary 47L05
Published electronically:
June 13, 2011
MathSciNet review:
2823023
Fulltext PDF
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Abstract: The length of a pair of matrices is the smallest integer such that words in the matrices with at most factors span the unital algebra generated by the pair. Upper bounds for lengths have been much studied. If is a rank one (complex) matrix, the length of the irreducible pair is and the subwords of form a basis for . New examples are given of irreducible pairs of matrices of length . There exists an irreducible pair of matrices of length . We begin the study of determining lower bounds for lengths.
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Additional Information
W. E. Longstaff
Affiliation:
School of Mathematics & Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
Email:
longstaf@maths.uwa.edu.au
Peter Rosenthal
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
Email:
rosent@math.toronto.edu
DOI:
http://dx.doi.org/10.1090/S000299392011111493
Keywords:
Length,
words
Received by editor(s):
March 1, 2010
Published electronically:
June 13, 2011
Communicated by:
Marius Junge
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
