Linear operators that preserve term ranks of Boolean matrices

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 talk, we give characterizations of linear operators that preserve term ranks of Boolean matrices (and matrices over antinegative semirings). That is, we show that a linear operator T on Boolean matrices (and matrix space over antinegative semirings) preserves term rank if and only if T preserves any two term ranks k and h if and only if T strongly preserves any one term rank k.