dc.contributor.author García Planas, María Isabel dc.contributor.author Klymchuk, Tetiana dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2018-09-26T11:49:13Z dc.date.issued 2018 dc.identifier.citation Garcia-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.issn 2444-8656 dc.identifier.other http://cervantes.up4sciences.org/lookInside/perturbation_analysis_of_a_matrix_differential_equation_dotx__abx.pdf dc.identifier.uri http://hdl.handle.net/2117/121517 dc.description.abstract Two 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.extent 8 p. dc.language.iso eng dc.publisher UP4, Institute of Sciences, S.L. dc.rights Attribution-NonCommercial-NoDerivs 3.0 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística dc.subject.lcsh Perturbation (Mathematics) dc.subject.lcsh Matrices--Mathematical models dc.subject.other Contragredient equivalence dc.subject.other Miniversal deformation dc.subject.other Perturbation dc.title Perturbation analysis of a matrix differential equation ¿x=ABx dc.type Article dc.subject.lemac Pertorbació (Matemàtica) dc.subject.lemac Matrius (Matemàtica) dc.contributor.group Universitat Politècnica de Catalunya. SCL-EG - Sistemes de Control Lineals: estudi Geomètric dc.identifier.doi 10.21042/AMNS.2018.1.00007 dc.description.peerreviewed Peer Reviewed dc.relation.publisherversion http://journals.up4sciences.org/applied_mathematics_and_nonlinear_sciences.html dc.rights.access Restricted access - publisher's policy local.identifier.drac 23307269 dc.description.version Postprint (author's final draft) dc.date.lift 10000-01-01 local.citation.author Garcia-Planas, M.I.; Klymchuk, T. local.citation.publicationName Applied Mathematics and Nonlinear Sciences local.citation.volume 3 local.citation.number 1 local.citation.startingPage 97 local.citation.endingPage 104
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