Linear Algebra By Kunquan Lan -fourth Edition- Pearson 2020 May 2026

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

We can create the matrix $A$ as follows:

Using the Power Method, we can compute the PageRank scores as: Linear Algebra By Kunquan Lan -fourth Edition- Pearson 2020

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.

$v_0 = \begin{bmatrix} 1/3 \ 1/3 \ 1/3 \end{bmatrix}$ $A = \begin{bmatrix} 0 & 1/2 & 0

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.

$v_2 = A v_1 = \begin{bmatrix} 1/4 \ 1/2 \ 1/4 \end{bmatrix}$ $v_2 = A v_1 = \begin{bmatrix} 1/4 \

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