Combinatorial Types of Tropical Eigenvectors
classification
🧮 math.CO
cs.DM
keywords
theytropicalcombinatorialconeconesdecompositiondetermineeigenvalue-eigenvector
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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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