In mathematics, a Metzler matrix is a matrix in which all the off-diagonal components are nonnegative (equal to or greater than zero): It is named after the American economist Lloyd Metzler.
Metzler matrices appear in stability analysis of time delayed differential equations and positive linear dynamical systems.
In mathematics, especially linear algebra, a matrix is called Metzler, quasipositive (or quasi-positive) or essentially nonnegative if all of its elements are non-negative except for those on the main diagonal, which are unconstrained.
-matrices, as a Z-matrix is equivalent to a negated quasipositive matrix.
This is natural, once one observes that the generator matrices of continuous-time Markov chains are always Metzler matrices, and that probability distributions are always non-negative.