Linear operators that preserve perimeters of Boolean matrices

摘要

For a Boolean rank $1$ matrix $A = {f ab}^t ,$ we define the perimeter of $A$ as the number of nonzero entries in both $f a$ and $f b$. The perimeter of an $m imes n$ Boolean matrix $A$ is the minimum of the perimeters of the rank-1 decompositions of $A$. In this article we characterize the linear operators that preserve the perimeters of Boolean matrices.