A real square matrix A {\displaystyle A} is monotone if for all real vectors v {\displaystyle v}, A v ≥ 0 {\displaystyle Av\geq 0} implies v ≥ 0 {\displaystyle v\geq 0}, where ≥ {\displaystyle \geq } is the element-wise order on R n {\displaystyle \mathbb {R} ^{n}}. Wikipedia