A positive matrix is one whose entries are positive.
An $m\times n$ matrix $M$ is positive if each entry $m_{ij}>0$, $1\leq i\leq m,1\leq j\leq n$; the closely related term non-negative allows for the case $m_{ij}\geq 0$ (see nonnegative-matrices). Note that this is not the same notion as positive definite: $\pmatrix{5&4\\ 3&2}$ is positive but not positive definite and $\pmatrix{5&4\\ -3&2}$ is positive definite but not positive.
Non-negative matrices are more common (for example, as transition matrices in Markov chains) but positive matrices are interesting in their own right. For instance, the Perron-Frobenius theorem asserts the existence of a unique largest positive eigenvalue of positive matrices.
