On tropical Kleene star matrices and alcoved polytopes

zbMath1297.15029arXiv1210.1735MaRDI QIDQ5409922

M. J. de la Puente

Publication date: 15 April 2014

Full work available at URL: https://arxiv.org/abs/1210.1735

zbMATH Keywords

convex setsmatrix normstropical algebraalcoved polytopesKleene star matricesnormal idempotent matrices

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Max-plus and related algebras (15A80)

Related Items

Multivariate volume, Ehrhart, and \(h^\ast \)-polynomials of polytropes ⋮ A congruence on the semiring of normal tropical matrices ⋮ Orthogonality for \((0, -1)\) tropical normal matrices ⋮ Certain congruences on the semiring of normal tropical matrices ⋮ Normal tropical \((0,-1)\)-matrices and their orthogonal sets ⋮ Isocanted alcoved polytopes. ⋮ Quasi-Euclidean classification of alcoved convex polyhedra ⋮ Matrices commuting with a given normal tropical matrix ⋮ Approximating the volume of tropical polytopes is difficult ⋮ Tropical implementation of the analytical hierarchy process decision method ⋮ Distances on the tropical line determined by two points ⋮ Convexity of tropical polytopes ⋮ On the groups associated with a tropical \(n\times n\) matrix

Cites Work

• Unnamed Item
• Pure dimension and projectivity of tropical polytopes
• Symmetric alcoved polytopes
• Max-plus definite matrix closures and their eigenspaces
• Generators, extremals and bases of max cones
• On visualization scaling, subeigenvectors and Kleene stars in max algebra
• Minimax algebra and applications
• Duality and separation theorems in idempotent semimodules.
• Simple image set of (max,+) linear mappings
• Max-algebra: The linear algebra of combinatorics?
• Tropical convexity
• Bases in max-algebra
• Computing the vertices of tropical polyhedra using directed hypergraphs
• Alcoved polytopes. I.
• Tropical and Idempotent Mathematics
• Tropical and ordinary convexity combined
• Max-linear Systems: Theory and Algorithms
• The Hungarian Method for the Assignment Problem
• Asymptotics of the Perron eigenvalue and eigenvector using max-algebra
• Idempotent tropical matrices and finite metric spaces
• Idempotent Mathematics and Mathematical Physics
• A Note on a Generalization of Boolean Matrix Theory