In this paper we consider so-called Google matrices and show that all eigenvalues ($lambda$) of them have a fundamental property $|lambda|leq 1$. The stochastic eigenvector corresponding to $lambda=1$ called the PageRank vector plays a central role in the Googles software. We study it in detail and present some important problems. The purpose of the paper is to make {bf the heart of Google} clearer for undergraduates.
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