Linear Algebra By Kunquan Lan -fourth Edition- Pearson 2020 〈NEWEST — 2027〉

Page 1 links to Page 2 and Page 3 Page 2 links to Page 1 and Page 3 Page 3 links to Page 2

Suppose we have a set of 3 web pages with the following hyperlink structure: Linear Algebra By Kunquan Lan -fourth Edition- Pearson 2020

Imagine you're searching for information on the internet, and you want to find the most relevant web pages related to a specific topic. Google's PageRank algorithm uses Linear Algebra to solve this problem. Page 1 links to Page 2 and Page

The basic idea is to represent the web as a graph, where each web page is a node, and the edges represent hyperlinks between pages. The PageRank algorithm assigns a score to each page, representing its importance or relevance. The PageRank algorithm assigns a score to each

The PageRank scores are computed by finding the eigenvector of the matrix $A$ corresponding to the largest eigenvalue, which is equal to 1. This eigenvector represents the stationary distribution of the Markov chain, where each entry represents the probability of being on a particular page.

$v_1 = A v_0 = \begin{bmatrix} 1/6 \ 1/2 \ 1/3 \end{bmatrix}$