Bulletin of the
Korean Mathematical Society BKMS

For a Boolean rank $1$ matrix $A = {\bf ab}^t ,$ we define the perimeter of $A$ as the number of nonzero entries in both $\bf a$ and $\bf b$. The perimeter of an $m \times n$ 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.

Keywords: Boolean linear operator, perimeter, (U,V)-operator, term rank

MSC numbers: 15A03, 15A04