While such matrices are commonly found, the term "positive matrix" is only occasionally used due to the possible confusion with positive-definite matrices, which are different.
Eigenvalues and eigenvectors of square positive matrices are described by the Perron–Frobenius theorem.
The inverse of any non-singular M-matrix [clarification needed] is a non-negative matrix.
If the non-singular M-matrix is also symmetric then it is called a Stieltjes matrix.
There are a number of groups of matrices that form specializations of non-negative matrices, e.g. stochastic matrix; doubly stochastic matrix; symmetric non-negative matrix.