Zero-term rank preservers^∗

^∗This work was supported by Korea Research Foundation Grant (KRF-99-015-DI0003)

Abstract

We obtain characterizations of those linear operators that preserve zero-term rank on the m×n matrices over antinegative semirings. That is, a linear operator T preserves zero-term rank if and only if it has the form T(X)=P(B∘X)Q, where P, Q are permutation matrices and B∘X is the Schur product with B whose entries are all nonzero and not zero-divisors.

Keywords:

• Linear operator
• Zero-term rank
• AMS Subject Classifications: 15A03, 15A04

^∗This work was supported by Korea Research Foundation Grant (KRF-99-015-DI0003)

^∗This work was supported by Korea Research Foundation Grant (KRF-99-015-DI0003)

Notes

^∗This work was supported by Korea Research Foundation Grant (KRF-99-015-DI0003)