Volume 37 • Number 3 • 2014   • Linear Operators that Preserve Term Ranks of Matrices over Semirings Leroy B. Beasley and Seok-Zun Song Abstract. The term rank of a matrix $A$ is the least number of lines (rows or columns) needed to include all the nonzero entries in $A$, and is a well-known upper bound for many standard and non-standard matrix ranks, and is one of the most important combinatorially. In this paper, we obtain a characterization of linear operators that preserve term ranks of matrices over antinegative semirings. That is, we show that a linear operator $T$ on a matrix space over antinegative semirings preserves term rank if and only if $T$ preserves any two term ranks $k$ and $l$ if and only if $T$ strongly preserves any one term rank $k$. 2010 Mathematics Subject Classification: 15A86, 15A03, 15A04 Full text: PDF