# Lyapunov transformation

From Encyclopedia of Mathematics

A non-degenerate linear transformation (or ), smoothly depending on a parameter , that satisfies the condition

It was introduced by A.M. Lyapunov in 1892 (see [1]). The Lyapunov transformation is widely used in the theory of linear systems of ordinary differential equations. In many cases the requirement

can be discarded.

#### References

[1] | A.M. Lyapunov, "Stability of motion" , Acad. Press (1966) (Translated from Russian) |

#### Comments

#### References

[a1] | W. Hahn, "Stability of motion" , Springer (1967) pp. 422 |

**How to Cite This Entry:**

Lyapunov transformation.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Lyapunov_transformation&oldid=11223

This article was adapted from an original article by V.M. Millionshchikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article