Quadratic realizability of palindromic matrix polynomials

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dc.contributor.author Terán Vergara, Fernando de
dc.contributor.author Martínez Dopico, Froilán César
dc.contributor.author Mackey, D. Steven
dc.contributor.author Perović, Vasilije
dc.date.accessioned 2021-04-06T10:06:02Z
dc.date.available 2021-04-15T23:00:04Z
dc.date.issued 2019-04-15
dc.identifier.bibliographicCitation De Terán, F., Dopico, F. M., Mackey, D. S. & Perović, V. (2019). Quadratic realizability of palindromic matrix polynomials. Linear Algebra and Its Applications, 567, pp. 202–262.
dc.identifier.issn 0024-3795
dc.identifier.uri http://hdl.handle.net/10016/32270
dc.description.abstract Let L = (L-1 , L-2) be a list consisting of a sublist L(1 )of powers of irreducible (monic) scalar polynomials over an algebraically closed field F, and a sublist L-2 of nonnegative integers. For an arbitrary such list L, we give easily verifiable necessary and sufficient conditions for L to be the list of elementary divisors and minimal indices of some T-palindromic quadratic matrix polynomial with entries in the field F. For L satisfying these conditions, we show how to explicitly construct a T-palindromic quadratic matrix polynomial having L as its structural data; that is, we provide a T-palindromic quadratic realization of L. Our construction of T-palindromic realizations is accomplished by taking a direct sum of low bandwidth T-palindromic blocks, closely resembling the Kronecker canonical form of matrix pencils. An immediate consequence of our in-depth study of the structure of T-palindromic quadratic polynomials is that all even grade T-palindromic matrix polynomials have a T-palindromic strong quadratification. Finally, using a particular Mobius transformation, we show how all of our results can be easily extended to quadratic matrix polynomials with T-even structure.
dc.format.extent 61
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2019 Published by Elsevier Inc.
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Matrix polynomials
dc.subject.other Quadratic realizability
dc.subject.other Elementary divisors
dc.subject.other Minimal indices
dc.subject.other Quasi-canonical form
dc.subject.other Quadratifications
dc.subject.other T-palindromic
dc.subject.other Inverse problem
dc.title Quadratic realizability of palindromic matrix polynomials
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1016/j.laa.2019.01.003
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2012-32542
dc.relation.projectID Gobierno de España. MTM2015-68805-REDT
dc.relation.projectID Gobierno de España. MTM2015-65798-P
dc.relation.projectID Gobierno de España. MTM2017-90682-REDT
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 202
dc.identifier.publicationlastpage 262
dc.identifier.publicationtitle Linear Algebra and Its Applications
dc.identifier.publicationvolume 567
dc.identifier.uxxi AR/0000023338
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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