Most tutorials on complex topics are apparently written by very smart people whose goal is to use as little space as possible and who assume that their readers already know almost as much as the author does. This tutorial’s not like that. It’s more a manifestivus for the rest of us. It’s about the mechanics of singular value decomposition, especially as it relates to some techniques in natural language processing. It’s written by someone who knew zilch about singular value decomposition or any of the underlying math before he started writing it, and knows barely more than that now. Accordingly, it’s a bit long on the background part, and a bit short on the truly explanatory part, but hopefully it contains all the information necessary for someone who’s never heard of singular value decomposition before to be able to do it.
An excellent place to start. And check out the animation at wikipedia.