Generic symmetric matrix polynomials with bounded rank and fixed odd grade

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dc.contributor.author Terán Vergara, Fernando de
dc.contributor.author Dmytryshyn, Andrii
dc.contributor.author Martínez Dopico, Froilán César
dc.date.accessioned 2021-04-07T10:50:34Z
dc.date.available 2021-04-07T10:50:34Z
dc.date.issued 2020-07-16
dc.identifier.bibliographicCitation De Terán, F., Dmytryshyn, A. & Dopico, F. M. (2020). Generic Symmetric Matrix Polynomials with Bounded Rank and Fixed Odd Grade. SIAM Journal on Matrix Analysis and Applications, 41(3), pp. 1033–1058.
dc.identifier.issn 0895-4798
dc.identifier.uri http://hdl.handle.net/10016/32293
dc.description.abstract We determine the generic complete eigenstructures for n x n complex symmetric matrix polynomials of odd grade d and rank at most r. More precisely, we show that the set of n x n complex symmetric matrix polynomials of odd grade d , i.e., of degree at most d, and rank at most r is the union of the closures of the rd/2 +1 sets of symmetric matrix polynomials having certain, explicitly described, complete eigenstructures. Then we prove that these sets are open in the set of n x n complex symmetric matrix polynomials of odd grade d and rank at most r. In order to prove the previous results, we need to derive necessary and sufficient conditions for the existence of symmetric matrix polynomials with prescribed grade, rank, and complete eigenstructure in the case where all their elementary divisors are different from each other and of degree 1. An important remark on the results of this paper is that the generic eigenstructures identified in this work are completely different from the ones identified in previous works for unstructured and skew-symmetric matrix polynomials with bounded rank and fixed grade larger than 1, because the symmetric ones include eigenvalues while the others not. This difference requires using new techniques.
dc.format.extent 26
dc.language.iso eng
dc.publisher Society for Industrial and Applied Mathematics (SIAM)
dc.rights © 2020, Society for Industrial and Applied Mathematics
dc.subject.other Complete eigenstructure
dc.subject.other Matrix polynomials
dc.subject.other Symmetry
dc.subject.other Normal rank
dc.subject.other Orbits
dc.subject.other Bundles
dc.subject.other Genericity
dc.subject.other Pencils
dc.title Generic symmetric matrix polynomials with bounded rank and fixed odd grade
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1137/19M1294964
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2015-65798-P
dc.relation.projectID Gobierno de España. PID2019-106362GB-I00
dc.relation.projectID Gobierno de España. MTM2017-90682-REDT
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 1033
dc.identifier.publicationissue 3
dc.identifier.publicationlastpage 1058
dc.identifier.publicationtitle SIAM Journal on Matrix Analysis and Applications
dc.identifier.publicationvolume 41
dc.identifier.uxxi AR/0000026775
dc.contributor.funder Ministerio de Economía y Competitividad (España)
dc.contributor.funder Agencia Estatal de Investigación (España)
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