Universal bounds for matrix semigroups
Volume 203 / 2011
Studia Mathematica 203 (2011), 69-77
MSC: Primary 15A30; Secondary 15A60.
DOI: 10.4064/sm203-1-4
Abstract
We show that any compact semigroup of $n\times n$ matrices is similar to a semigroup bounded by $\sqrt{n}$. We give examples to show that this bound is best possible and consider the effect of the minimal rank of matrices in the semigroup on this bound.
