Geodesic
Universal bounds for positive matrix semigroups
Leo Livshits1 ; Gordon MacDonald2 ; Laurent Marcoux3 ; Heydar Radjavi3
1Department of Mathematics Colby College Waterville, ME 04901, U.S.A.
2School of Mathematical and Computational Sciences University of Prince Edward Island Charlottetown, PE, C1A 4P3, Canada
3Department of Pure Mathematics University of Waterloo Waterloo, ON, N2L 3G1, Canada
Studia Mathematica, Tome 232 (2016) no. 2, pp. 143-153
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 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.
DOI : 10.4064/sm8421-3-2016
Keywords: compact semigroup positive times matrices similar via positive diagonal similarity semigroup bounded sqrt examples bound best possible consider effect additional conditions semigroup obtain improved bounds cases

Leo Livshits  1   ; Gordon MacDonald  2   ; Laurent Marcoux  3   ; Heydar Radjavi  3

1 Department of Mathematics Colby College Waterville, ME 04901, U.S.A.
2 School of Mathematical and Computational Sciences University of Prince Edward Island Charlottetown, PE, C1A 4P3, Canada
3 Department of Pure Mathematics University of Waterloo Waterloo, ON, N2L 3G1, Canada 
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Leo Livshits; Gordon MacDonald; Laurent Marcoux; Heydar Radjavi. Universal bounds for positive matrix semigroups. Studia Mathematica, Tome 232 (2016) no. 2, pp. 143-153. doi: 10.4064/sm8421-3-2016

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