Three notions of tropical rank for symmetric matrices

Details Three notions of tropical rank for symmetric matrices Three notions of tropical rank for symmetric matrices

2009-12-08

arxiv.org/abs/0912.1411v1

Mathematics

Combinatorics

23 pages, 3 figures

Scientific paper

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.

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