Quasipositive matrix

In mathematics, especially linear algebra, a matrix is called quasipositive if all of its elements are non-negative except for those on the main diagonal, which are unconstrained. That is, a quasipositive matrix is any matrix "A" which satisfies

:$$A=(a_{ij});quad a_{ij}geq 0, quad i eq j.

Quasipositive matrices are also sometimes referred to as $$Z^{(-)}-matrices, as a "Z"-matrix is equivalent to a negated quasipositive matrix.

The exponential of a quasipositive matrix is a nonnegative matrix.