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Combinatorial Types of Tropical Eigenvectors (1105.5504v3)
Published 27 May 2011 in math.CO and cs.DM
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.
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