Almost-reducible linear system

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of ordinary differential equations

A system


having the following property: There exist a system , , with constant coefficients and, for every , a Lyapunov transformation such that by the change of variables , the system (*) is transformed into the system


Every reducible linear system is almost reducible.


[1] N.A. Izobov, "Linear systems of ordinary differential equations" J. Soviet Math. , 5 : 1 (1976) pp. 46–96 Itogi Nauk. i Tekhn. Mat. Anal. , 12 (1974) pp. 71–146
How to Cite This Entry:
Almost-reducible linear system. V.M. Millionshchikov (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098