Positivity and matrix semigroups (Q616415)

The authors consider positivity of complex matrix semigroups. The main result states that given an irreducible group \(G\), if the diagonal entries of the matrices of \(G\) are nonnegative, then the group \(G\) is positivizable, that is: there is a change of basis such that the matrices of \(G\) have nonnegative entries. Furthermore, by means of an example for the case of the matrices of \(G\) being of order 3, it is shown that even with the condition that the trace be equal or greater than zero together with that only one of the diagonal elements be negative, it is not enough to guarantee that an irreducible group of matrices be positivizable.