Combinatorial Types of Tropical Eigenvectors

Details Combinatorial Types of Tropical Eigenvectors Combinatorial Types of Tropical Eigenvectors

2011-05-27

arxiv.org/abs/1105.5504v3

Mathematics

Combinatorics

9 pages, 1 figure, exposition improved

Scientific paper

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.

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