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| DOI | 10.13001/ELA.2024.8441 | ||||
| Año | 2024 | ||||
| Tipo | artículo de investigación |
Citas Totales
Autores Afiliación Chile
Instituciones Chile
% Participación
Internacional
Autores
Afiliación Extranjera
Instituciones
Extranjeras
A spectrum A = { lambda (1) , . . . , lambda (n) } of complex numbers is said to be realizable if it is the spectrum of an entrywise nonnegative matrix A. The spectrum A is diagonalizably realizable ( DR ) if the realizing matrix A is diagonalizable, and A is universally realizable ( UR ) if it is realizable for each possible Jordan canonical form allowed by A. In 1981, Minc proved that if A is the spectrum of a diagonalizable positive matrix, then A is universally realizable. One of the main open questions about the problem of universal realizability of spectra is whether DR implies UR . Here, we prove a surprisingly simple result, which shows how diagonalizably realizable implies universally realizable.
| Ord. | Autor | Género | Institución - País |
|---|---|---|---|
| 1 | Marijuan, C. | Hombre |
UNIV VALLADOLID - España
Universidad de Valladolid - España |
| 2 | SOTO-MONTERO, RICARDO LORENZO | Hombre |
Universidad Católica del Norte - Chile
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| Fuente |
|---|
| European Regional Development Fund |
| Universidad Católica del Norte |
| Ministerio de Ciencia, Innovacion y Universidades |
| Agencia Estatal de Investigación |
| Núcleo |
| MCIU/AEI |
| Universidad Catolica del Norte-VRIDT |
| ERDF "A way of making Europe" |
| NUCLEO UCN, Chile |
| Agradecimiento |
|---|
| Partially supported by grant PID2022-138906NB-C21 funded by MCIU/AEI/10.13039/501100011033 and by ERDF "A way of making Europe", and by Universidad Catolica del Norte-VRIDT 036-2020, NUCLEO UCN VRIDT-083-2020, Chile. |
| \u2217Received by the editors on January 4, 2024. Accepted for publication on April 4, 2024. Handling Editor: Helena Smigoc. Corresponding Author: Carlos Mariju\u00E1n. Funding: Partially supported by grant PID2022-138906NB-C21 funded by MCIU/AEI/ 10.13039/501100011033 and by ERDF \u201CA way of making Europe\u201D, and by Universidad Cat\u00F3lica del Norte-VRIDT 036-2020, NUCLEO UCN VRIDT-083-2020, Chile. \u2020Department of Matem\u00E1tica Aplicada, Universidad de Valladolid, Spain (cmarijuan@uva.es). \u2021Department of Matem\u00E1ticas, Universidad Cat\u00F3lica del Norte, Antofagasta, Chile (rsoto@ucn.cl). |
| \u2217Received by the editors on January 4, 2024. Accepted for publication on April 4, 2024. Handling Editor: Helena Smigoc. Corresponding Author: Carlos Mariju\u00E1n. Funding: Partially supported by grant PID2022-138906NB-C21 funded by MCIU/AEI/ 10.13039/501100011033 and by ERDF \u201CA way of making Europe\u201D, and by Universidad Cat\u00F3lica del Norte-VRIDT 036-2020, NUCLEO UCN VRIDT-083-2020, Chile. \u2020Department of Matem\u00E1tica Aplicada, Universidad de Valladolid, Spain (cmarijuan@uva.es). \u2021Department of Matem\u00E1ticas, Universidad Cat\u00F3lica del Norte, Antofagasta, Chile (rsoto@ucn.cl). |