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Journal Articles Linear Algebra and its Applications Year : 2020

Tropical planar networks

Abstract

We show that every tropical totally positive matrix can be uniquely represented as the transfer matrix of a canonical totally connected weighted planar network. We deduce a uniqueness theorem for the factorization of a tropical totally positive in terms of elementary Jacobi matrices.

Dates and versions

hal-02423904 , version 1 (26-12-2019)

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Stéphane Gaubert, Adi Niv. Tropical planar networks. Linear Algebra and its Applications, 2020, 595, pp.123-144. ⟨10.1016/j.laa.2020.02.019⟩. ⟨hal-02423904⟩
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