Journal of the
Korean Mathematical Society JKMS

The term rank of a matrix $A$ is the least number of lines (rows or columns) needed to include all the nonzero entries in $A$. In this paper, we obtain a characterization of linear transformations that preserve term ranks of matrices over antinegative semirings. That is, we show that a linear transformation $T$ from a matrix space into another matrix space over antinegative semirings preserves term rank if and only if $T$ preserves any two term ranks $k$ and $l$.

Keywords: semiring, term rank, linear transformation

MSC numbers: Primary 15A86, 15A03, 15A04