Abstract

Google's success derives in large part from its PageRank algorithm, which ranks the importance of web pages 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 project 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.

MSC codes

  1. 15-01
  2. 15A18
  3. 15A51

Keywords

  1. linear algebra
  2. PageRank
  3. eigenvector
  4. stochastic matrix

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References

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Abraham Berman, Robert Plemmons, Nonnegative matrices in the mathematical sciences, Academic Press [Harcourt Brace Jovanovich Publishers], 1979xviii+316, Computer Science and Applied Mathematics
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Carl Meyer, Matrix analysis and applied linear algebra, Society for Industrial and Applied Mathematics (SIAM), 2000xii+718, With 1 CD‐ROM (Windows, Macintosh and UNIX) and a solutions manual (iv+171 pp.)
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C. Moler, The World’s Largest Matrix Computation, http://www.mathworks.com/company/newsletters/news_notes/clevescorner/oct02_cleve.html (August 1, 2005).
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Published In

cover image SIAM Review
SIAM Review
Pages: 569 - 581
ISSN (online): 1095-7200

History

Published online: 3 August 2006

MSC codes

  1. 15-01
  2. 15A18
  3. 15A51

Keywords

  1. linear algebra
  2. PageRank
  3. eigenvector
  4. stochastic matrix

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