J. C. Holladay and Richard S. Varga, On powers of non-negative matrices, Proc. Amer. Math. Soc. 9 (1958), 631-634. MR 20, 3885. Zbl. 96, p. 8.

Let A=||a_{i,j} || be an n x n matrix consisting of non-negative
elements. It is well known [1, p. 463] that A is primitive if and only if, for
some positive integer n, A^{n} has all its elements positive. One needs
to know only this property of primitive matrices to understand this paper. If A^{k}
is positive (i.e. has all its elements positive), then A^{h} is also
positive for all integers h>k [1, p. 463]. 2 Letting A be primitive, we
shall define γ(A) as the smallest positive integer
h such that A_{h} is positive.