Interpreting a vector expression

[wofsy]

In R^3 I have two vectors a and b and the operator D = (d/dx,d/dy,d/dz)

What is the interpretation/ picture of (aD)b - (bD)a? This is another vector.

 

[Ben Niehoff]

You mean a geometrical interpretation? It's the Lie derivative, ${\mathcal L}_A B$.

 

[wofsy]

You mean a geometrical interpretation? It's the Lie derivative, ${\mathcal L}_A B$.

thanks. That's all I need.