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

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

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

We can create the matrix $A$ as follows: $A = \begin{bmatrix} 0 & 1/2 & 0

The PageRank scores indicate that Page 2 is the most important page, followed by Pages 1 and 3. To compute the eigenvector, we can use the

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.

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