Geodesic
Universal bounds for matrix semigroups
Leo Livshits1 ; Gordon MacDonald2 ; Heydar Radjavi3
1Department of Mathematics Colby College Waterville, ME 04901, U.S.A.
2Department of Mathematics and Statistics University of Prince Edward Island Charlottetown, PE, Canada C1A 4P3
3Department of Pure Mathematics University of Waterloo Waterloo, ON, Canada N2L 3G1
Studia Mathematica, Tome 203 (2011) no. 1, pp. 69-77
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm203-1-4
Keywords: compact semigroup times matrices similar semigroup bounded sqrt examples bound best possible consider effect minimal rank matrices semigroup bound

Leo Livshits  1   ; Gordon MacDonald  2   ; Heydar Radjavi  3

1 Department of Mathematics Colby College Waterville, ME 04901, U.S.A.
2 Department of Mathematics and Statistics University of Prince Edward Island Charlottetown, PE, Canada C1A 4P3
3 Department of Pure Mathematics University of Waterloo Waterloo, ON, Canada N2L 3G1 
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Leo Livshits; Gordon MacDonald; Heydar Radjavi. Universal bounds for matrix semigroups. Studia Mathematica, Tome 203 (2011) no. 1, pp. 69-77. doi: 10.4064/sm203-1-4

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