Livshits, LeoMacDonald, GordonMarcoux, LaurentRadjavi, Heydar2020-04-022020-04-022016https://doi.org/10.4064/sm8421-3-2016http://hdl.handle.net/10012/15736Version of record at https://doi.org/10.4064/sm8421-3-2016We 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.enpositive matrix semigroupsArticle