English

Combinatorial Types of Tropical Eigenvectors

Combinatorics 2014-02-26 v3 Discrete Mathematics

Abstract

The map which takes a square matrix to its tropical eigenvalue-eigenvector pair is piecewise linear. We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we also study the restriction of that cone decomposition to the subspace of skew-symmetric matrices.

Keywords

Cite

@article{arxiv.1105.5504,
  title  = {Combinatorial Types of Tropical Eigenvectors},
  author = {Bernd Sturmfels and Ngoc Mai Tran},
  journal= {arXiv preprint arXiv:1105.5504},
  year   = {2014}
}

Comments

9 pages, 1 figure, exposition improved

R2 v1 2026-06-21T18:13:31.338Z