On totally nonpositive matrices associated with a triple negatively realizable
[EN] Let A is an element of R-nxn be a totally nonpositive matrix (t.n.p.) with rank r and principal rank p, that is, every minor of A is nonpositive and p is the size of the largest invertible principal submatrix of A. We introduce that a triple (n, r, p) will be called negatively realizable if the...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/180470 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/180470 |
| Access Level: | acceso abierto |
| Palabra clave: | Totally nonpositive matrix Principal rank Triple negatively realizable Linear algebra MATEMATICA APLICADA |
| Sumario: | [EN] Let A is an element of R-nxn be a totally nonpositive matrix (t.n.p.) with rank r and principal rank p, that is, every minor of A is nonpositive and p is the size of the largest invertible principal submatrix of A. We introduce that a triple (n, r, p) will be called negatively realizable if there exists a t.n.p. matrix A of order n and such that its rank is r and its principal rank is p. In this work we extend the results obtained for irreducible totally nonnegative matrices given in Canto and Urbano (Linear Algebra Appl 551:125-146. https://doi.org/10.1016/j.laa.2018.03.045, 2018) to t.n.p. matrices. For that, we consider the sequence of the first p-indices of A and study the linear dependence relations between their rows and columns. These relations allow us to construct t.n.p. matrices associated with a triple (n, r, p) negatively realizable and a specific sequence of the first p-indices. |
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