Bijective linear rank preservers for spaces of matrices over antinegative semirings

Abstract

We classify the bijective linear operators on spaces of matrices over antinegative commutative semirings with no zero divisors which preserve certain rank functions such as the symmetric rank, the factor rank and the tropical rank. We also classify the bijective linear operators on spaces of matrices over the max-plus semiring which preserve the Gondran–Minoux row rank or the Gondran–Minoux column rank.