Pekkle sent me a link a while ago to an article at AMS about how Google determines the importance of a page, also known as its pagerank. It’s actually a very interesting paper and a pleasure to read, especially the first few pages where the author takes you through some elementary logic to arrive at an elegantly simple representation of the entire world wide web’s pageranks as the eigenvector of a square matrix described simply by the number of links on each page. If you’re like me and derive gratification from seeing real world problems reduced to abstract mathematical constructs, you’ll have a blast with this one. I also found this short review of eigenvalues and eigenvectors helpful, as it’s been a while since I’ve touched any linear algebra.