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Universal bounds for positive matrix semigroups

Volume 232 / 2016

Leo Livshits, Gordon MacDonald, Laurent Marcoux, Heydar Radjavi Studia Mathematica 232 (2016), 143-153 MSC: Primary 15A30; Secondary 15A21. DOI: 10.4064/sm8421-3-2016 Published online: 23 March 2016

Abstract

We show that any compact semigroup of positive $n\times n$ matrices is similar (via a positive diagonal similarity) to a semigroup bounded by $\sqrt {n}$. We give examples to show this bound is best possible. We also consider the effect of additional conditions on the semigroup and obtain improved bounds in some cases.

Authors

  • Leo LivshitsDepartment of Mathematics
    Colby College
    Waterville, ME 04901, U.S.A.
    e-mail
  • Gordon MacDonaldSchool of Mathematical and Computational Sciences
    University of Prince Edward Island
    Charlottetown, PE, C1A 4P3, Canada
    e-mail
  • Laurent MarcouxDepartment of Pure Mathematics
    University of Waterloo
    Waterloo, ON, N2L 3G1, Canada
    e-mail
  • Heydar RadjaviDepartment of Pure Mathematics
    University of Waterloo
    Waterloo, ON, N2L 3G1, Canada
    e-mail

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