On the Kapranov ranks of tropical matrices

DOI10.1016/j.laa.2011.11.004zbMath1243.15013arXiv1207.4697OpenAlexW2065371460MaRDI QIDQ417453

Yaroslav N. Shitov

Publication date: 14 May 2012

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.4697

zbMATH Keywords

semigrouptropical semiringtropical matricesKapranov ranktropical rankinfinite ground fieldrank-product inequality

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Miscellaneous inequalities involving matrices (15A45) Semirings (16Y60) Vector spaces, linear dependence, rank, lineability (15A03) Max-plus and related algebras (15A80)

Related Items (3)

Rank functions of tropical matrices ⋮ A separation between tropical matrix ranks ⋮ Mixed subdivisions and ranks of tropical matrices

Cites Work

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• The \(4\times 4\) minors of a \(5\times n\) matrix are a tropical basis
• Inequalities for Gondran-Minoux rank and idempotent semirings
• Example of the matrix of size \((6\times 6)\) with different tropical rank and Kapranov rank
• Linear independence over tropical semirings and beyond
• RANK INEQUALITIES OVER SEMIRINGS
• A Catalogue of Combinatorial Geometries
• Kapranov rank vs. tropical rank

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