The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
The $25,000,000,000 Eigenvector: The Linear Algebra behind Google
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.
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Cites
The anatomy of a large-scale hypertextual Web search engine
Brin, S., & Page, L. (1998) · Computer Networks and ISDN Systems · doi:10.1016/s0169-7552(98)00110-x · Cited by 16,004
Nonnegative Matrices in the Mathematical Sciences
(1979) · Elsevier eBooks · doi:10.1016/c2013-0-10361-3 · Cited by 5,451
Matrix Analysis and Applied Linear Algebra
Meyer, C. (2000) · doi:10.1137/1.9780898719512 · Cited by 3,565
Matrix analysis and applied linear algebra
(2001) · Choice Reviews Online · doi:10.5860/choice.38-5065 · Cited by 3,300
Introduction to the Numerical Solution of Markov Chains
Stewart, W. J. (1995) · Princeton University Press eBooks · doi:10.1515/9780691223384 · Cited by 1,750
Langville, A., & Meyer, C. (2004) · Internet Mathematics · doi:10.1080/15427951.2004.10129091 · Cited by 894
Bianchini, M., Gori, M., & Scarselli, F. (2005) · ACM Transactions on Internet Technology · doi:10.1145/1052934.1052938 · Cited by 539
A Survey of Eigenvector Methods for Web Information Retrieval
Langville, A. N., & Meyer, C. D. (2005) · SIAM Review · doi:10.1137/s0036144503424786 · Cited by 430
Adaptive methods for the computation of PageRank
Kamvar, S., Haveliwala, T., & Golub, G. (2004) · Linear Algebra and its Applications · doi:10.1016/j.laa.2003.12.008 · Cited by 271
Farahat, A., LoFaro, T., Miller, J. C., Rae, G., & Ward, L. A. (2006) · SIAM Journal on Scientific Computing · doi:10.1137/s1064827502412875 · Cited by 117
Cited by
Structural Properties of the Caenorhabditis elegans Neuronal Network
Varshney, L. R., Chen, B. L., Paniagua, E., Hall, D. H., & Chklovskii, D. B. (2011) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1001066 · Cited by 867
Metadata
- Authors
- Bryan, K., & Leise, T.
- Venue
- SIAM Review
- Published
- 2006-01
- Volume
- 48
- Issue
- 3
- Pages
- 569-581
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W1996934732
- Cited by
- 260
- References
- 11
- FWCI
- 6.49
- Type
- journal article
- Language
- en
- Open access
- closed
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