All Jordan canonical forms of irreducible totally non-negative matrices
| Autor: | Begoña Cantó, Ana M. Urbano, Rafael Cantó |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Algebra and Number Theory
Minor (linear algebra) Irreducible matrix 010103 numerical & computational mathematics 01 natural sciences law.invention Combinatorics Principal rank Matrix (mathematics) Invertible matrix law Jordan canonical form Rank (graph theory) Totally non-negative matrix Canonical form 0101 mathematics MATEMATICA APLICADA Mathematics |
| Zdroj: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname |
| DOI: | 10.1080/03081087.2019.1676691 |
| Popis: | [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 This research was partially supported by the Ministerio de Economia y Competitividad under the Spanish DGI grant MTM2017-85669-P-AR |
| Databáze: | OpenAIRE |
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