Column stochastic matrix/Definition

A real square matrix

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

is called column stochastic matrix if all entries

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

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

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