The \(4\times 4\) minors of a \(5\times n\) matrix are a tropical basis

DOI10.1016/j.laa.2010.09.032zbMath1231.14053arXiv0912.5264OpenAlexW1482907961MaRDI QIDQ550661

Elena Rubei, Melody Chan, Anders Nedergaard Jensen

Publication date: 13 July 2011

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

Full work available at URL: https://arxiv.org/abs/0912.5264

zbMATH Keywords

Kapranov ranktropical ranktropical bases

Mathematics Subject Classification ID

Related Items

Rank functions of tropical matrices, A separation between tropical matrix ranks, Tropical Gaussians: a brief survey, When do the \(r\)-by-\(r\) minors of a matrix form a tropical basis?, Tropical positivity and determinantal varieties, On matrices with different tropical and Kapranov ranks, On the Kapranov ranks of tropical matrices, Isotropical linear spaces and valuated Delta-matroids, Detecting tropical defects of polynomial equations, Mixed subdivisions and ranks of tropical matrices

Uses Software

• cdd
• SoPlex
• Gfan

Cites Work

• Unnamed Item
• Unnamed Item
• The space of tropically collinear points is shellable
• How to draw tropical planes
• Tropical hyperplane arrangements and oriented matroids
• A tropical approach to secant dimensions
• Computing tropical varieties
• TROPICAL POLYHEDRA ARE EQUIVALENT TO MEAN PAYOFF GAMES
• Linear independence over tropical semirings and beyond
• Tropical Linear Spaces
• The Tropical Rank of a Tropical Matrix
• The tropical Grassmannian
• A Catalogue of Combinatorial Geometries
• Kapranov rank vs. tropical rank
• Introduction to tropical algebraic geometry