Google’s success derives in large part from its PageRank algorithm, which ranks the importance of webpages according to an eigenvector of a weighted link matrix. Analysis of the PageRank formula provides a wonderful applied topic for a linear algebra course. Instructors may assign this article as a pro ject to more advanced students, or spend one or two lectures presenting the material with assigned homework from the exercises. This material also complements the discussion of Markov chains in matrix algebra. Maple and Mathematica files supporting this material can be found at www.rose-hulman.edu/`bryan
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Thanks for the Interesting document, and that it might be used as a study piece.
Nobody knows how the current formula works, it changes all the time and the relationship between the index and the web is a complex adaptive system, therefore inherently unpredictable
Andy Roberts twitter