2009/12/08 by Dustin Cartwright, Cartwright, Dustin, Melody Chan +1
Computer Science · Mathematics · #14T05 #Combinatorics (math.CO) #FOS: Mathematics #Matrix Theory and Algorithms #Polynomial and algebraic computation #Tensor decomposition and applications #math.CO #msc:14T05
paper · pdf · doi:10.48550/arxiv.0912.1411
23 pages, 3 figures
arxiv created 2009/12/08 · openalex publication_date 2009/12/08 · arxiv updated 2010/01/07 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We introduce and study three different notions of tropical rank for symmetric and dissimilarity matrices in terms of minimal decompositions into rank 1 symmetric matrices, star tree matrices, and tree matrices. Our results provide a close study of the tropical secant sets of certain nice tropical varieties, including the tropical Grassmannian. In particular, we determine the dimension of each secant set, the convex hull of the variety, and in most cases, the smallest secant set which is equal to the convex hull.