Geodesic
Universal bounds for matrix semigroups
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
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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