Monotone matrix

A real square matrix ${\displaystyle A}$ is monotone (in the sense of Collatz) if for all real vectors ${\displaystyle v}$, ${\displaystyle Av\geq 0}$ implies ${\displaystyle v\geq 0}$, where ${\displaystyle \geq }$ is the element-wise order on ${\displaystyle \mathbb {R} ^{n}}$.