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Planar networks and inequalities on eigenvalues

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Defense Thèse de doctorat : Univ. Genève, 2012 - Sc. 4458 - 2012/08/17
Abstract In this thesis we study the relation between two problems of linear algebra concerning eigenvalues of Hermitian matrices and certain planar graphs: the Horn problem of describing the set of eigenvalues of sums of Hermitian matrices and the Gelfand-Zeitlin problem of describing the set of eigenvalues of Hermitian matrices and their principle submatrices. Both sets are polyhedral cones. We introduce a combinatorial framework where the same cones arise naturally. We also give some explaination of this unexpected relation and generalize our construction to arbitrary positive semirings.
Keywords Horn problemGelfand-Zeitlin problemPlanar networksTropical limits
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URN: urn:nbn:ch:unige-238472
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PODKOPAEVA, Maria. Planar networks and inequalities on eigenvalues. Université de Genève. Thèse, 2012. https://archive-ouverte.unige.ch/unige:23847

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Deposited on : 2012-11-07

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