Displaying similar documents to “Unique prime factorization in a partial semigroup of matrix-polynomials”

Universal bounds for positive matrix semigroups

Leo Livshits, Gordon MacDonald, Laurent Marcoux, Heydar Radjavi (2016)

Studia Mathematica

Similarity:

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.

Universal bounds for matrix semigroups

Leo Livshits, Gordon MacDonald, Heydar Radjavi (2011)

Studia Mathematica

Similarity:

We show that any compact semigroup of n × n matrices is similar to a semigroup bounded by √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.