Stochastic matrix

A matrix $P \in M_{n \times m}(\mathbb{R})$ is called stochastic if for all $i \in \mathbb{Z}$ with $1 \leq i \leq n$ we have

$$ \sum_{j = 1}^m p_{i,j} = 1$$

and for $1 \leq i \leq n$ and $1 \leq j \leq m$ we have $0 \leq p_{i,j} \leq 1$. Therefore every row forms a probability distribution.