Eigenvectors and eigenvalues explained visually
Very beautiful graphs, but i don't think it's going to make people understand anything. 
I would start with the problem : easily compute sums of dependant values, then show a naive computation, then use matrices, vectors and eigenvalues to come to a solution, and only then, show a graphical representation of the steps performed.I'm surprised that this post isn't following this method, because i've come to think it's the standard way of explaining scientific things in the US.