Basic solutions of systems with two max-linear inequalities

DOI10.1016/j.laa.2011.02.033zbMath1227.15018arXiv1002.0758OpenAlexW1996442824MaRDI QIDQ550677

Yong-Cai Geng, Sumit K. Garg

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/1002.0758

zbMATH Keywords

max algebraextremal raytropical algebrabasic solutionsKleene starsmultiorder principle

Mathematics Subject Classification ID

Linear inequalities of matrices (15A39) Vector spaces, linear dependence, rank, lineability (15A03) Max-plus and related algebras (15A80)

Related Items

Weakly linear systems for matrices over the max-plus quantale, An improved algorithm for finding the generators of the solution space for \(A\otimes \mathbf{x}\ge \mathbf{x} \), Complete solution of tropical vector inequalities using matrix sparsification., An algorithm to describe the solution set of any tropical linear system \(A \odot x = B \odot x\), On \(2 \times 2\) tropical commuting matrices

Cites Work

• Tropical linear maps on the plane
• The Minkowski theorem for max-plus convex sets
• Generators, extremals and bases of max cones
• A decomposition formula of idempotent polyhedral cones based on idempotent superharmonic spaces
• Moduloïds and pseudomodules. I: Dimension theory
• Tropical convexity
• Multiorder, Kleene stars and cyclic projectors in the geometry of max cones
• Max-plus convex sets and max-plus semispaces. II
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