<bos><start_of_turn>system
You are a helpful AI assistant.
lista de codigos linguisticos disponibles: ["de", "en"].<end_of_turn>
<start_of_turn>user
Erklärt den Page Rank-Algorithmus.<end_of_turn>
<start_of_turn>model
The Page algorithm was developed by Google, and it was primarily what distinguished Google from the competition. This allows you to order a set of web pages according to their relevance or importance.
The algorithm consists of the following:
1. Firstly, on the web we have pages that have references or links to other pages. This can be seen as a directed graph in which each page represents a vertex, and each link represents a directed edge.
2. Given a set of candidate pages, which we want to order according to a ranking, we do a random walk on the graph (every time we are at a vertex, we choose one of the vertex's outgoing edges randomly).
3. This process is a Markov chain, and the probability of ending at any vertex can be modeled with a vector (one entry per vertex).
4. The process of taking a random step is equivalent to multiplying the vector by a constant Markov matrix (the sum of the values ​​in each column is 1).
5. The priority of each vertex will be given by the probability of ending at said vertex after an infinite number of steps.
6. Markov matrices have several properties that allow us to guarantee that said number exists. If said matrix is ​​A, then the product of $A^\infty$ and any vector converges to the eigenvector whose eigenvalue is 1. Furthermore, Markov matrices satisfy the property that the largest eigenvalue is 1.
Given that, the page rank algorithm finds said eigenvector, and with it obtains the probability of ending at any vertex.
7. With these values, the web pages are ordered.<end_of_turn><eos>