I did like this. There is a certain elegance[1] to diagram based descriptions of mathematical/physical concepts.

Another that is maybe more similar in that it removes a lot of dummy variables(indices in this case) is the Penrose graphical notation[2] for tensors. I have actually never calculated anything using these diagrams so I don't know how practical they are.

[1]:http://en.wikipedia.org/wiki/Feynman_diagram [2]:http://en.wikipedia.org/wiki/Penrose_graphical_notation