Swordmaster Dragon
I think there are some very important applications of eigenvalues in engineering, but the ones that I know of are all in quantum mechanics and computer graphics. Actually, the Wikipedia page on eigenvectors has a short list of applications of this stuff. It *is* pretty kewl.
Indeed. The original paper by Page and Brin isn't much to get excited about, but check out the formula for pagerank through wikipedia. Though, note that they are computing a left-hand eigenvalue using the power method, and a formula from Matrix analysis called the Sherron-Morrison rank one update formula. I did my Math major senior research project on Pagerank last fall. Very interesting.
A good book on the topic is "Pagerank and Beyond" written by Meyer. He also wrote a graduate level textbook on Applied Linear Algebra and Matrix analysis which I have worn to death. Though is you want to understand the whole search process and the vector space model of search, you're going to need to look up the groundbreaking paper by Salton "A blueprint for automatic text indexing"
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