Differential Geometry 15 : The Lie product - part 2

In this lecture we explore a useful property of the Lie bracket - where we explore brackets of products of functions and vector fields. We then prove a very important result - the fact that coordinate basis vector fields have mutually vanishing Lie brackets. We then make us of these properties to derive an expression for the components of a Lie bracket in the coordinate basis. We end with an example of application of these results.