Editing Vector field (section)

===The Lie bracket===
The flows associated to two vector fields need not [[commutative property|commute]] with each other. Their failure to commute is described by the [[Lie bracket of vector fields|Lie bracket]] of two vector fields, which is again a vector field. The Lie bracket has a simple definition in terms of the action of vector fields on smooth functions <math>f</math>:
:<math>[X,Y](f):=X(Y(f))-Y(X(f)).</math>