Linear Algebra By Kunquan Lan -fourth Edition- Pearson 2020

The converged PageRank scores are:

The PageRank scores indicate that Page 2 is the most important page, followed by Pages 1 and 3. Linear Algebra By Kunquan Lan -fourth Edition- Pearson 2020

$v_k = \begin{bmatrix} 1/4 \ 1/2 \ 1/4 \end{bmatrix}$ The converged PageRank scores are: The PageRank scores

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. such as eigenvalues and eigenvectors

We can create the matrix $A$ as follows:

To compute the eigenvector, we can use the Power Method, which is an iterative algorithm that starts with an initial guess and repeatedly multiplies it by the matrix $A$ until convergence.