2026-04-14T06:47:56Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/1215172026-02-08T04:42:48Zcom_2072_1033col_2072_452950

Perturbation analysis of a matrix differential equation ¿x=ABx García Planas, María Isabel Klymchuk, Tetiana Àrees temàtiques de la UPC::Matemàtiques i estadística Perturbation (Mathematics) Matrices--Mathematical models Contragredient equivalence Miniversal deformation Perturbation Pertorbació (Matemàtica) Matrius (Matemàtica) 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) Peer Reviewed Postprint (author's final draft) 2018 Article http://journals.up4sciences.org/applied_mathematics_and_nonlinear_sciences.html http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Restricted access - publisher's policy Attribution-NonCommercial-NoDerivs 3.0 Spain UP4, Institute of Sciences, S.L.