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