Mixed subdivisions and ranks of tropical matrices

DOI10.1090/S0002-9939-2013-11766-1zbMath1278.15004OpenAlexW1970334482MaRDI QIDQ2862165

Yaroslav N. Shitov

Publication date: 14 November 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2013-11766-1

zbMATH Keywords

tropical semiringmixed subdivisionKapranov ranktropical matrixBarvinok rank

Mathematics Subject Classification ID

Vector spaces, linear dependence, rank, lineability (15A03) Max-plus and related algebras (15A80)

Related Items (2)

A separation between tropical matrix ranks ⋮ The arctic rank of a Boolean matrix

Cites Work

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• On the Kapranov ranks of tropical matrices
• The \(4\times 4\) minors of a \(5\times n\) matrix are a tropical basis
• Example of the matrix of size \((6\times 6)\) with different tropical rank and Kapranov rank
• Linear independence over tropical semirings and beyond

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