In this paper, we consider so-called Google matrices and show that all eigenvalues  of them have a fundamental property  The stochastic eigenvector corresponding to  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 the heart of Google clearer for undergraduates.

Google matrices, eigenvalue 1, PageRank vector, linear algebra.