Zero-term rank and zero-star cover number of symmetric matrices and their linear preservers

摘要

This paper concerns two notions of matrix functions over semirings; zero-term rank and zero-star cover number. We study linear operators that preserve these two matrix functions of n x n symmetric matrices. Consequently, we determine the form of linear operators T on n x n symmetric matrices that preserves zeroterm rank (zero-star cover number). We also show that a linear operator T on symmetric matrices preserves zero-term rank (zero-star cover number) if and only if T preserves zero-term ranks (zero-star cover numbers, respectively) 1 and 2. Other characterizations of zero-term rank (zero-star cover number, respectively) preservers are also given.