Universal bounds for positive matrix semigroups
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We show that any compact semigroup of positive n×n matrices is similar (via a positive diagonal similarity) to a semigroup bounded by 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.
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Leo Livshits, Gordon MacDonald, Laurent Marcoux, Heydar Radjavi (2016). Universal bounds for positive matrix semigroups. UWSpace. http://hdl.handle.net/10012/15736