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

$v_0 = \begin{bmatrix} 1/3 \ 1/3 \ 1/3 \end{bmatrix}$

$A = \begin{bmatrix} 0 & 1/2 & 0 \ 1/2 & 0 & 1 \ 1/2 & 1/2 & 0 \end{bmatrix}$ Linear Algebra By Kunquan Lan -fourth Edition- Pearson 2020

Let's say we have a set of $n$ web pages, and we want to compute the PageRank scores. We can create a matrix $A$ of size $n \times n$, where the entry $a_{ij}$ represents the probability of transitioning from page $j$ to page $i$. If page $j$ has a hyperlink to page $i$, then $a_{ij} = \frac{1}{d_j}$, where $d_j$ is the number of hyperlinks on page $j$. If page $j$ does not have a hyperlink to page $i$, then $a_{ij} = 0$. $v_0 = \begin{bmatrix} 1/3 \ 1/3 \ 1/3

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. If page $j$ does not have a hyperlink

This story is related to the topics of Linear Algebra, specifically eigenvalues, eigenvectors, and matrix multiplication, which are covered in the book "Linear Algebra" by Kunquan Lan, Fourth Edition, Pearson 2020.

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