## Linear Algebra in Ranking Algorithms.

When we learned about the ranking algorithm in class, we used simple algebra and intuition to create a series of equations to solve our long-time equilibrium solution. How do we achieve this using a standardized method with computers? Ultimately, the millions of web pages are too big for humans to handle and a standard method that computers can use is needed. We look to linear algebra for our answer.

http://online.sfsu.edu/meredith/Linear_Algebra/725_F2010/PDF/Dynneson_FinalDraft_Linear-Algebra-Project.pdf
The first idea is to use Markov chains to create a stochastic model for the page ranking algorithm. The idea is that a matrix represents the pages, and repeated calculations of the matrix using linear algebra should result in an equilibrium similar to the one discussed in class. In the matrix, let a[i,j] represent the row i and column j. a[i,j] also represents if there is a link connected from j to i. If there is not, this value is 0, if there is, this value is non-zero. The columns must add up to 1 so each a[i,j] in column 3, for example, must add up to 1 evenly. This will then be repeatedly calculated to find the equilibrium.