Nonnegative matrix

A nonnegative matrix is a matrix where all the elements are equal to or above zero

$\mathbf {X} \geq 0,\qquad \forall _{ij}\,x_{ij}\geq 0$

The set of positive matrices is a subset of all nonnegative matrices.

A non-negative matrix can represent a transision matrix for a Markov chain.

A rectangular nonnegative matrix can be approximated by a decomposition with two other nonnegative matrix via non-negative matrix factorization.