Surjective linear transformations of tropical matrices preserving transitive closures. (English) Zbl 1511.15022
Summary: In this paper we characterize those surjective linear transformations of tropical matrices preserving the set of all weak transitive closures \(M^W_n\) and the set of all strong transitive closures \(M^S_n\), respectively. We illustrate that there exist non-surjective linear transformations that preserve \(M^W_n\) or \(M^S_n\). Also, we consider the strongly linear preservers of \(M^W_n\) and \(M^S_n\), respectively.
MSC:
| 15A80 | Max-plus and related algebras |
| 15A86 | Linear preserver problems |
| 15A04 | Linear transformations, semilinear transformations |
| 14T10 | Foundations of tropical geometry and relations with algebra |
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