Linear transformations of tropical matrices preserving the cyclicity index

We combine matrix theory and graph theory methods to give a complete characterization of the surjective linear transformations of tropical matrices that preserve the cyclicity index. We show that there are non-surjective linear transformations that preserve the cyclicity index and we leave it open t...

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Bibliographic Details
Published inSpecial matrices Vol. 9; no. 1; pp. 112 - 118
Main Authors Guterman, Alexander, Kreines, Elena, Thomassen, Carsten
Format Journal Article
LanguageEnglish
Published De Gruyter Open 01.03.2021
De Gruyter
Subjects
cyclicity index
linear preservers
tropical linear algebra
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Summary:We combine matrix theory and graph theory methods to give a complete characterization of the surjective linear transformations of tropical matrices that preserve the cyclicity index. We show that there are non-surjective linear transformations that preserve the cyclicity index and we leave it open to characterize those.
ISSN:2300-7451
2300-7451
DOI:10.1515/spma-2020-0128