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 2021-03-18T09:38:05Z 2021-03-18T09:38:05Z 2015
dc.identifier.bibliographicCitation De Terán, F., Dopico, F. M., Van Dooren, P. (2015). Matrix Polynomials with Completely Prescribed Eigenstructure. SIAM Journal on Matrix Analysis and Applications, 36(1), pp. 302–328.
dc.identifier.issn 0895-4798
dc.description.abstract We present necessary and sufficient conditions for the existence of a matrix polynomial when its degree, its finite and infinite elementary divisors, and its left and right minimal indices are prescribed. These conditions hold for arbitrary infinite fields 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 fix 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.format.extent 27
dc.language.iso eng
dc.publisher Society for Industrial and Applied Mathematics (SIAM)
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-ifications
dc.subject.other Minimal indices
dc.subject.other Inverse polynomial eigenvalue problems
dc.title Matrix Polynomials with Completely Prescribed Eigenstructure
dc.type article
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2012-32542
dc.type.version acceptedVersion
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 AR/0000018798
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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