Column stochastic matrix/Definition

Column stochastic matrix

A real square matrix

${}M={\left(a_{ij}\right)}_{1\leq i,j\leq n}\,$

is called a column stochastic matrix if all entries

${}a_{ij}\geq 0\,,$

and every column sum (that is, for every ${}j$), is

${}\sum _{i=1}^{n}a_{ij}=1\,.$