Google and eigenvalues. We describe the Pagerank algorithm, which was one of the algorithms used by Google for their search engine. For this, we rank the websites using an importance vector vector and write the system as a Markov chain, using matrices. Then we diagonalize the matrix using linear algebra, more precisely eigenvalues and eigenvectors. Finally, by taking limits of the matrix, we can determine which website reigns supreme. This probably has applications in data science and neural networks as well.

Matrix Limits and Markov Chains:    • Matrix Limits and Markov Chains  
Diagonalization:    • Diagonalize 3x3 matrix  

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