An explicit description of the irreducible components of the set of matrix pencils with bounded normal rank

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dc.contributor.author Terán Vergara, Fernando de
dc.contributor.author Martínez Dopico, Froilán César
dc.contributor.author Landsberg, J.M.
dc.date.accessioned 2021-01-19T12:22:07Z
dc.date.available 2021-01-19T12:22:07Z
dc.date.issued 2017-05-01
dc.identifier.bibliographicCitation De Terán, F., Dopico, F. M., & Landsberg, J. M. (2017). An explicit description of the irreducible components of the set of matrix pencils with bounded normal rank. Linear Algebra and its Applications, 520, 80-103.
dc.identifier.issn 0024-3795
dc.identifier.uri http://hdl.handle.net/10016/31726
dc.description.abstract The set of m x n singular matrix pencils with normal rank at most r is an algebraic set with r + 1 irreducible components. These components are the closure of the orbits (under strict equivalence) of r 1 matrix pencils which are in Kronecker canonical form. In this paper, we provide a new explicit description of each of these irreducible components which is a parametrization of each component. Therefore one can explicitly construct any pencil in each of these components. The new description of each of these irreducible components consists of the sum of r rank-1 matrix pencils, namely, a column polynomial vector of degree at most 1 times a row polynomial vector of degree at most 1, where we impose one of these two vectors to have degree zero. The number of row vectors with zero degree determines each irreducible component. (C) 2017 Elsevier Inc. All rights reserved.
dc.language.iso eng
dc.publisher Elsevier
dc.rights © Elsevier, 2017
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 pencil
dc.subject.other Normal rank
dc.subject.other Algebraic set
dc.subject.other Irreducible components
dc.subject.other Orbits
dc.subject.other Kronecker canonical form
dc.subject.other Perturbation-theory
dc.subject.other Geometric approach
dc.subject.other Canonical form
dc.subject.other Orbit
dc.title An explicit description of the irreducible components of the set of matrix pencils with bounded normal rank
dc.type research article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1016/j.laa.2017.01.021
dc.rights.accessRights open access
dc.identifier.publicationfirstpage 80
dc.identifier.publicationlastpage 103
dc.identifier.publicationtitle Linear Algebra and its Applications
dc.identifier.publicationvolume 520
dc.identifier.uxxi AR/0000019724
dc.affiliation.dpto UC3M. Departamento de Matemáticas
dc.affiliation.grupoinv UC3M. Grupo de Investigación: Matemática Aplicada a Control, Sistemas y Señales
dc.type.hasVersion AM
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