-fourth Edition- Pearson 2020: Linear Algebra By Kunquan Lan

The Google PageRank algorithm is a great example of how Linear Algebra is used in real-world applications. By representing the web as a graph and using Linear Algebra techniques, such as eigenvalues and eigenvectors, we can compute the importance of each web page and rank them accordingly.

We can create the matrix $A$ as follows:

Page 1 links to Page 2 and Page 3 Page 2 links to Page 1 and Page 3 Page 3 links to Page 2 Linear Algebra By Kunquan Lan -fourth Edition- Pearson 2020

$v_k = \begin{bmatrix} 1/4 \ 1/2 \ 1/4 \end{bmatrix}$

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 Google PageRank algorithm is a great example

$A = \begin{bmatrix} 0 & 1/2 & 0 \ 1/2 & 0 & 1 \ 1/2 & 1/2 & 0 \end{bmatrix}$

Suppose we have a set of 3 web pages with the following hyperlink structure: The PageRank algorithm assigns a score to each

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.

The converged PageRank scores are: