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Reducibility of Nonautonomous Linear Differential Equations
Author(s) -
Siegmund Stefan
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610701002897
Subject(s) - integrable system , mathematics , eigenvalues and eigenvectors , linear differential equation , diagonal , system of linear equations , linear system , jordan matrix , matrix (chemical analysis) , differential equation , mathematical analysis , diagonal matrix , block (permutation group theory) , block matrix , pure mathematics , function (biology) , combinatorics , physics , geometry , materials science , quantum mechanics , evolutionary biology , composite material , biology
A linear autonomous system of differential equations ẋ = Ax can be transformed to its Jordan normal form, that is, the transformed system is in block diagonal form and the blocks correspond to different eigenvalues. This result is generalized to arbitrary nonautonomous linear systems ẋ = A ( t ) x with a locally integrable matrix function A:R → R N × N .