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Universal bounds for matrix semigroups

Tom 203 / 2011

Leo Livshits, Gordon MacDonald, Heydar Radjavi Studia Mathematica 203 (2011), 69-77 MSC: Primary 15A30; Secondary 15A60. DOI: 10.4064/sm203-1-4

Streszczenie

We show that any compact semigroup of $n\times n$ matrices is similar to a semigroup bounded by $\sqrt{n}$. We give examples to show that this bound is best possible and consider the effect of the minimal rank of matrices in the semigroup on this bound.

Autorzy

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

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