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Eventually positive matrices with rational eigenvectors†

Published online by Cambridge University Press:  19 September 2008

David Handelman
David Handelman
Affiliation:
Department of Mathematics, Faculty of Science, University of Ottawa, Ottawa, Ontario, Canada
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Abstract

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Let A be an n × n real matrix; sufficient conditions were previously worked out, assuming non-commensurability of eigenvectors, for A to be SL(n, )-conjugate to a matrix all sufficiently large powers of which have strictly positive entries. We show that when the ‘large’ eigenvectors are commensurable and satisfy the obvious necessary conditions, then A is also going to be so conjugate. In particular, we deduce, if A is a rational matrix with large eigenvalue exceeding 1 and of multiplicity one, then A is algebraically shift equivalent to an eventually positive matrix, using only integer rectangular matrices.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 2 , June 1987 , pp. 193 - 196
Copyright
Copyright © Cambridge University Press 1987

References

REFERENCE

[H]Handelman, D.. Positive integral matrices and C* algebras affiliated to topological Markov Chains. J. Operator Theory 6 (1981), 55–74.Google Scholar