Matrix polynomials with completely prescribed eigenstructure

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Show simple item record Terán Vergara, Fernando de Martínez Dopico, Froilán César Van Dooren, Paul 2015-12-03T14:25:53Z 2015-12-03T14:25:53Z 2014-07
dc.identifier.bibliographicCitation SIAM Journal on Matrix Analysis and Applications, 36 (2015) 1, pp. 302-328.
dc.identifier.issn 0895-4798 (Print)
dc.identifier.issn 1095-7162 (Online)
dc.description The proceeding at: Joint ALAMA-GAMM/ANLA 2014 Meeting, took place 2014, July 14-16, in Barcelona (Spain).
dc.description.abstract We present necessary and su cient conditions for the existence of a matrix polynomial when its degree, its nite and in nite elementary divisors, and its left and right minimal indices are prescribed. These conditions hold for arbitrary in nite elds and are determined mainly by the \index sum theorem", which is a fundamental relationship between the rank, the degree, the sum of all partial multiplicities, and the sum of all minimal indices of any matrix polynomial. The proof developed for the existence of such polynomial is constructive and, therefore, solves a very general inverse problem for matrix polynomials with prescribed complete eigenstructure. This result allows us to x the problem of the existence of (l)-ifications of a given matrix polynomial, as well as to determine all their possible sizes and eigenstructures.
dc.description.sponsorship This research was partially supported by the Ministerio de Economía y Competitividad of Spain through grant MTM-2012-32542 and by the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office.
dc.format.extent 27
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Society for Industrial and Applied Mathematics
dc.rights © 2015 Society for Industrial and Applied Mathematics
dc.subject.other Matrix polynomials
dc.subject.other Index sum theorem
dc.subject.other Invariant polynomials
dc.subject.other (l)-cations
dc.subject.other Minimal indices
dc.subject.other Inverse polynomial eigenvalue problems.
dc.title Matrix polynomials with completely prescribed eigenstructure
dc.type article
dc.type conferenceObject
dc.description.status Publicado
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1137/140964138
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM-2012-32542
dc.type.version publishedVersion
dc.relation.eventdate 2014, July 14-16
dc.relation.eventplace Barcelona (Spain)
dc.relation.eventtitle Joint ALAMA-GAMM/ANLA 2014 Meeting
dc.relation.eventtype proceeding
dc.identifier.publicationfirstpage 302
dc.identifier.publicationissue 1
dc.identifier.publicationlastpage 328
dc.identifier.publicationtitle SIAM Journal on Matrix Analysis and Applications
dc.identifier.publicationvolume 36
dc.identifier.uxxi CC/0000022782
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