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Google's PageRank and Beyond by Carl D. Meyer, Amy N. Langville

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Chapter Seven

The PageRank Problem as a Linear System

Abraham Lincoln, in his humorous, self-deprecating style, said “If I were two-faced, would I be wearing this one?” Honest Abe wasn’t, but the PageRank problem is two-faced. There’s the eigenvector face it was given by its parents, Brin and Page, at birth, and there’s the linear system face, which can be arrived at with a little cosmetic surgery in the form of algebraic manipulation. Because Brin and Page originally conceived of the PageRank problem as an eigenvector problem (find the dominant eigenvector for the Google matrix), the eigenvector face has received much more press and fanfare. ...

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