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dc.contributor.authorGarcía Planas, María Isabel
dc.contributor.authorKlymchuk, Tetiana
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2018-09-26T11:49:13Z
dc.date.issued2018
dc.identifier.citationGarcia-Planas, M.I., Klymchuk, T. Perturbation analysis of a matrix differential equation ¿x=ABx. "Applied Mathematics and Nonlinear Sciences", 2018, vol. 3, núm. 1, p. 97-104.
dc.identifier.issn2444-8656
dc.identifier.otherhttp://cervantes.up4sciences.org/lookInside/perturbation_analysis_of_a_matrix_differential_equation_dotx__abx.pdf
dc.identifier.urihttp://hdl.handle.net/2117/121517
dc.description.abstractTwo complex matrix pairs (A,B) and (A',B') are contragrediently equivalent if there are nonsingular S and R such that (A',B')=(S-1AR,R-1BS). M.I. García-Planas and V.V. Sergeichuk (1999) constructed a miniversal deformation of a canonical pair (A,B) for contragredient equivalence; that is, a simple normal form to which all matrix pairs (A+˜A,B+˜B) close to (A,B) can be reduced by contragredient equivalence transformations that smoothly depend on the entries of ˜A and ˜B. Each perturbation (˜A,˜B) of (A,B) defines the first order induced perturbation A˜B+˜AB of the matrix AB, which is the first order summand in the product (A+˜A)(B+˜B)=AB+A˜B+˜AB+˜A˜B. We find all canonical matrix pairs (A,B), for which the first order induced perturbations A˜B+˜AB are nonzero for all nonzero perturbations in the normal form of García-Planas and Sergeichuk. This problem arises in the theory of matrix differential equations ¿x=Cx, whose product of two matrices: C=AB; using the substitution x=Sy, one can reduce C by similarity transformations S-1CS and (A,B) by contragredient equivalence transformations (S-1AR,R-1BS)
dc.format.extent8 p.
dc.language.isoeng
dc.publisherUP4, Institute of Sciences, S.L.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshPerturbation (Mathematics)
dc.subject.lcshMatrices--Mathematical models
dc.subject.otherContragredient equivalence
dc.subject.otherMiniversal deformation
dc.subject.otherPerturbation
dc.titlePerturbation analysis of a matrix differential equation ¿x=ABx
dc.typeArticle
dc.subject.lemacPertorbació (Matemàtica)
dc.subject.lemacMatrius (Matemàtica)
dc.contributor.groupUniversitat Politècnica de Catalunya. SCL-EG - Sistemes de Control Lineals: estudi Geomètric
dc.identifier.doi10.21042/AMNS.2018.1.00007
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttp://journals.up4sciences.org/applied_mathematics_and_nonlinear_sciences.html
dc.rights.accessRestricted access - publisher's policy
local.identifier.drac23307269
dc.description.versionPostprint (author's final draft)
dc.date.lift10000-01-01
local.citation.authorGarcia-Planas, M.I.; Klymchuk, T.
local.citation.publicationNameApplied Mathematics and Nonlinear Sciences
local.citation.volume3
local.citation.number1
local.citation.startingPage97
local.citation.endingPage104


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