On weak r-monotonicity
A real square matrix A is monotone iff Ax\(\geq 0\) implies \(x\geq 0\) (where the inequalities are entrywise). More generally, a real \(m\times n\) matrix A of order r is weak r-monotone if A has a monotone submatrix of order r. A real \(m\times n\) matrix A is \(\{\) \(1\}\)-monotone iff there is a nonnegative matrix X which satisfies the equation \(AXA=A\). These two generalizations of monotonicity are not equivalent in general. The author obtains a condition under which they are.
scientific article; zbMATH DE number 3979272