Linear Operators that Preserve Term Ranks of Matrices over Semirings

The term rank of a matrix ... is the least number of lines (rows or columns) needed to include all the nonzero entries in ..., 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 ... on a matrix space over antinegative semirings preserves term rank if and only if ... preserves any two term ranks ... and ... if and only if ... strongly preserves any one term rank ... 2010 Mathematics Subject Classification: 15A86, 15A03, 15A04 (ProQuest: ... denotes formulae omitted.)