# Almost-reducible linear system

From Encyclopedia of Mathematics

*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

where

Every reducible linear system is almost reducible.

#### References

[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: http://www.encyclopediaofmath.org/index.php?title=Almost-reducible_linear_system&oldid=18581

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098