On the characterization of totally nonpositive matrices
[EN] A nonpositive real matrix $A= (a_{ij})_{1 \leq i, j \leq n}$ is said to be totally nonpositive (negative) if all its minors are nonpositive (negative) and it is abbreviated as t.n.p. (t.n.). In this work a bidiagonal factorization of a nonsingular t.n.p. matrix $A$ is computed and it is stored...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| 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:10251/83249 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/83249 |
| Access Level: | acceso abierto |
| Palabra clave: | Totally nonpositive matrix Totally negative matrix Inverse Bidiagonal factorization MATEMATICA APLICADA |
| Sumario: | [EN] A nonpositive real matrix $A= (a_{ij})_{1 \leq i, j \leq n}$ is said to be totally nonpositive (negative) if all its minors are nonpositive (negative) and it is abbreviated as t.n.p. (t.n.). In this work a bidiagonal factorization of a nonsingular t.n.p. matrix $A$ is computed and it is stored in an matrix represented by $\mathcal{BD}_{(t.n.p.)}(A)$ when $a_{11}< 0$ (or $\mathcal{BD}_{(zero)}(A)$ when $a_{11}= 0$). As a converse result, an efficient algorithm to know if an matrix $\mathcal{BD}_{(t.n.p.)}(A)$ ($\mathcal{BD}_{(zero)}(A)$) is the bidiagonal factorization of a t.n.p. matrix with $a_{11}<0$ ($a_{11}= 0$) is given. Similar results are obtained for t.n. matrices using the matrix $\mathcal{BD}_{(t.n.)}(A)$, and these characterizations are extended to rectangular t.n.p. (t.n.) matrices. Finally, the bidiagonal factorization of the inverse of a nonsingular t.n.p. (t.n.) matrix $A$ is directly obtained from $\mathcal{BD}_{(t.n.p.)}(A)$ ($\mathcal{BD}_{(t.n.)}(A)$). |
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