A Superintroduction to Google Matrices for Undergraduates

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 Google's 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.