Spanning column ranks and their preservers of nonnegative matrices (Q677930)

Let \(U_+\) denote the nonnegative part of a unique factorization domain \(U\) in \(\mathbb{R}\) that has only one unit 1, and let \(M_{m,n}(U_+)\) be the set of \(m\times n\) matrices with entries in \(U_+\). If \(A\in M_{m,n}(U_+)\) is nonzero then the minimum number of columns of \(A\) that span its column space is called the spanning column rank of \(A\), and the zero matrix is said to have spanning column rank 0. The authors characterize the linear operators on \(M_{m,n} (U_+)\) that preserve spanning column rank.