Journal of the
Korean Mathematical Society JKMS

A rank one matrix can be factored as ${\bf u}^t{\bf v}$ for vectors ${\bf u}$ and ${\bf v}$ of appropriate orders. The perimeter of this rank one matrix is the number of nonzero entries in ${\bf u}$ plus the number of nonzero entries in ${\bf v}$. A matrix of rank $k$ is the sum of $k$ rank one matrices. The perimeter of a matrix of rank $k$ is the minimum of the sums of perimeters of the rank one matrices. In this article we characterize the linear operators that preserve perimeters of matrices over semirings.

Keywords: linear operator, perimeter, $(U,V)$-operator

MSC numbers: Primary 15A03, 15A04