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Combinatorica

, Volume 32, Issue 1, pp 55–84 | Cite as

Three notions of tropical rank for symmetric matrices

  • Dustin CartwrightEmail author
  • Melody Chan
Original Paper

Abstract

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.

Mathematics Subject Classification (2000)

52C99 

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Copyright information

© János Bolyai Mathematical Society and Springer Verlag 2012

Authors and Affiliations

  1. 1.Department of MathematicsYale UniversityNew HavenUSA
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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