Lyapunov transformation

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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.


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



[a1] W. Hahn, "Stability of motion" , Springer (1967) pp. 422
How to Cite This Entry:
Lyapunov transformation. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.M. Millionshchikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article