Publication: On bundles of matrix pencils under strict equivalence
dc.affiliation.dpto | UC3M. Departamento de Matemáticas | es |
dc.affiliation.grupoinv | UC3M. Grupo de Investigación: Matemática Aplicada a Control, Sistemas y Señales | es |
dc.contributor.author | Terán Vergara, Fernando de | |
dc.contributor.author | Martínez Dopico, Froilán César | |
dc.contributor.funder | Comunidad de Madrid | es |
dc.contributor.funder | Ministerio de Ciencia e Innovación (España) | es |
dc.contributor.funder | Universidad Carlos III de Madrid | es |
dc.date.accessioned | 2023-02-24T12:45:17Z | |
dc.date.available | 2023-02-24T12:45:17Z | |
dc.date.issued | 2023-02-01 | |
dc.description.abstract | Bundles of matrix pencils (under strict equivalence) are sets of pencils having the same Kronecker canonical form, up to the eigenvalues (namely, they are an infinite union of orbits under strict equivalence). The notion of bundle for matrix pencils was introduced in the 1990's, following the same notion for matrices under similarity, introduced by Arnold in 1971, and it has been extensively used since then. Despite the amount of literature devoted to describing the topology of bundles of matrix pencils, some relevant questions remain still open in this context. For example, the following two: (a) provide a characterization for the inclusion relation between the closures (in the standard topology) of bundles; and (b) are the bundles open in their closure? The main goal of this paper is providing an explicit answer to these two questions. In order to get this answer, we also review and/or formalize some notions and results already existing in the literature. We also prove that bundles of matrices under similarity, as well as bundles of matrix polynomials (defined as the set of m x n matrix polynomials of the same grade having the same spectral information, up to the eigenvalues) are open in their closure. | en |
dc.description.sponsorship | This work has been supported by the Agencia Estatal de Investigación of Spain through grants PID2019-106362GB-I00 MCIN/ AEI/10.13039/501100011033/ and MTM2017-90682-REDT, and by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation). | en |
dc.format.extent | 31 | |
dc.identifier.bibliographicCitation | De Terán, F., & Dopico, F. M. (2023). On bundles of matrix pencils under strict equivalence. Linear Algebra and its Applications, 658, 1-31. | en |
dc.identifier.doi | https://doi.org/10.1016/j.laa.2022.10.029 | |
dc.identifier.issn | 0024-3795 | |
dc.identifier.publicationfirstpage | 1 | |
dc.identifier.publicationlastpage | 31 | |
dc.identifier.publicationtitle | Linear Algebra and its Applications | en |
dc.identifier.publicationvolume | 658 | |
dc.identifier.uri | https://hdl.handle.net/10016/36669 | |
dc.identifier.uxxi | AR/0000032130 | |
dc.language.iso | eng | |
dc.publisher | Elsevier | en |
dc.relation.projectID | Gobierno de España. PID2019-106362GB-I00 | es |
dc.relation.projectID | Comunidad de Madrid. EPUC3M23 | es |
dc.relation.projectID | Gobierno de España. MTM2017-90682-REDT | es |
dc.relation.projectID | AT-2022 | |
dc.rights | © 2022 The Author(s). | en |
dc.rights | Atribución-NoComercial-SinDerivadas 3.0 España | * |
dc.rights.accessRights | open access | en |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.subject.eciencia | Matemáticas | es |
dc.subject.other | Matrix | en |
dc.subject.other | Matrix pencil | en |
dc.subject.other | Matrix polynomial | en |
dc.subject.other | Spectral information | en |
dc.subject.other | Strict equivalence | en |
dc.subject.other | Kronecker canonical form | en |
dc.subject.other | Jordan canonical form | en |
dc.subject.other | Orbit | en |
dc.subject.other | Bundle | en |
dc.subject.other | Open set | en |
dc.subject.other | Closure | en |
dc.subject.other | Majorization | en |
dc.title | On bundles of matrix pencils under strict equivalence | en |
dc.type | research article | * |
dc.type.hasVersion | VoR | * |
dspace.entity.type | Publication |
Files
Original bundle
1 - 1 of 1