Linear algebra and search engines

  • Jean-François ColletEmail author
Part of the Universitext book series (UTX)


The first five sections of this chapter develop the machinery necessary to give a purely linear-algebraic proof of the convergence theorem for ergodic chains on finite spaces. It is probably fair to say that the key property of the matrices (apart from being stochastic matrices) is positivity; this is why in order to make the presentation self-contained, most classical results on the Perron–Frobenius theory are included. The last section deals with the by now classical PageRank algorithm, which is included here because it is traditional to present it in the language of linear algebra rather than that of Markov processes.


Markov Matrices Strong Connectivity General Nonnegative Matrices Computing Page Rank Main Spectral Properties 
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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire J.A. DieudonnéUniversité de Nice Sophia-AntipolisNice Cedex 02France

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