Geodesic
Universal bounds for positive matrix semigroups
Leo Livshits1 ; Gordon MacDonald2 ; Laurent Marcoux3 ; Heydar Radjavi3
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
Studia Mathematica, Tome 232 (2016) no. 2, pp. 143-153

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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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