Universal bounds for positive matrix semigroups
Volume 232 / 2016
Studia Mathematica 232 (2016), 143-153
MSC: Primary 15A30; Secondary 15A21.
DOI: 10.4064/sm8421-3-2016
Published online: 23 March 2016
Abstract
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.
