Nonnegative matrices generating a finite cyclic group
Mordechai Lewin · Linear and Multilinear Algebra · 1977
It is shown that a nonnegative matrix A generates a cyclic group of order s if and only if it is the direct sum of cr of the form s being the l.c.m of their orders and each satisfying the equality being taken modulo cr . For s=2 this was shown by Harary and Minc.