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Tropical planar networks

Authors :: Adi Niv
Stéphane Gaubert
TROPICAL (TROPICAL)
Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP)
École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France
Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)
Kibbutzim College
The first author acknowledges the support of the Gaspard Monge (PGMO) program of Fondation Mathematique Hadamard, EDF, Orange and Thales, of the ICODE institute of Paris-Saclay, also of Labex Hadamard. This work started when the second author was with INRIA, being supported by the Chateaubriand program from the French Ministery of Foreign Affairs and by an INRIA fellowship
ANR-11-LABX-0056,LMH,LabEx Mathématique Hadamard(2011)
Source :: Linear Algebra and its Applications, Linear Algebra and its Applications, 2020, 595, pp.123-144. ⟨10.1016/j.laa.2020.02.019⟩, Linear Algebra and its Applications, Elsevier, 2020, 595, pp.123-144. ⟨10.1016/j.laa.2020.02.019⟩
Publication Year :: 2019
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.<br />Comment: The first author acknowledges the support of the Gaspard Monge (PGMO) program of Fondation Mathematique Hadamard, EDF, Orange and Thales, of the ICODE institute of Paris-Saclay, also of Labex Hadamard. This work started when the second author was with INRIA, being supported by the Chateaubriand program from the French Ministery of Foreign Affairs and by an INRIA fellowship

Details

Language :: English
ISSN :: 00243795
Database :: OpenAIRE
Journal :: Linear Algebra and its Applications, Linear Algebra and its Applications, 2020, 595, pp.123-144. ⟨10.1016/j.laa.2020.02.019⟩, Linear Algebra and its Applications, Elsevier, 2020, 595, pp.123-144. ⟨10.1016/j.laa.2020.02.019⟩
Accession number :: edsair.doi.dedup.....0c263f54496f0cff475b32cef49c193d
Full Text :: https://doi.org/10.1016/j.laa.2020.02.019⟩