2 problems

Let $m,n\geq2$, and let a real $m\times n$ matrix be semipositive if it maps some vector in $\mathbb{R}^n$ to a vector whose entries are all positive. An into linear preserver of s…

Dorsey et al.'s conjecture. If $L:M_{m,n}\to M_{m,n}$ is invertible and is an into preserver of $S(\mathbb{R}^n_+,\mathbb{R}^m_+)$, then there exist matrices $X$ and $Y$ such that