All Jordan canonical forms of irreducible totally non-negative matrices

[EN] Let be an irreducible totally non-negative matrix with rank r and principal rank p, that is, every minor of A is non-negative and p is the size of the largest invertible principal submatrix of A. Using Number Theory, we calculate the number of Jordan canonical forms of irreducible totally non-n...

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Bibliographic Details
Authors: Cantó Colomina, Begoña|||0000-0002-9837-3926, Cantó Colomina, Rafael|||0000-0002-1341-2800, Urbano Salvador, Ana María|||0000-0001-8590-1243
Format: article
Publication Date:2021
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/179419
Online Access:https://riunet.upv.es/handle/10251/179419
Access Level:Open access
Keyword:Totally non-negative matrix
Irreducible matrix
Principal rank
Jordan canonical form
MATEMATICA APLICADA
Description
Summary:[EN] Let be an irreducible totally non-negative matrix with rank r and principal rank p, that is, every minor of A is non-negative and p is the size of the largest invertible principal submatrix of A. Using Number Theory, we calculate the number of Jordan canonical forms of irreducible totally non-negative matrices associated with a realizable triple . Moreover, by using full rank factorizations of A and applying the Flanders theorem we obtain all these Jordan canonical forms. Finally, some algorithms associated with these results are given