A comparison of term ranks of symmetric matrices and their preservers

This paper concerns three notions of matrix functions over semirings; term rank, reduced term rank and star cover number. We compare these matrix functions and we study those linear operators that preserve these matrix functions of n×n symmetric matrices with zero diagonal. In particular, we obtain important characterizations of term-rank (reduced term rank, star cover number) preservers with respect to a term rank (a reduced term rank, a star cover number, respectively) and a special matrix.