How to prove this statement:
If $P = [p_{ij}]_{ 1 \leqslant i,j \leqslant m} \geqslant 0$ is a primitive matrix, then there exists a $k \in \mathbb{N}$ such that $ P^{k} > 0.$ Moreover $ P^{k+i}>0$ for all $ i = 1,2, \dots $
How to prove this statement:
If $P = [p_{ij}]_{ 1 \leqslant i,j \leqslant m} \geqslant 0$ is a primitive matrix, then there exists a $k \in \mathbb{N}$ such that $ P^{k} > 0.$ Moreover $ P^{k+i}>0$ for all $ i = 1,2, \dots $