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

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.

$v_k = \begin{bmatrix} 1/4 \ 1/2 \ 1/4 \end{bmatrix}$ 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 $a_{ij} = 0$. Imagine you're searching for information on the internet,

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. We can create a matrix $A$ of size