Linear algebra in the personal environment of Internet petitions (recommendations to: music, movies, books, shopping, etc.)

Abstract

When a website suggests a book, a movie, an article to acquaintances on a social network, it is making use of a referral system that makes suggestions based on the user's history and patterns of use and consumption. In this paper we show how recommendation systems use Linear Algebra concepts and tools. Recognizing this relationship makes possible the use of such systems as a didactic tool for the teaching of Linear Algebra, as it motivates significant learning and enriches the course material by providing concrete ideas upon which students can build an understanding of abstract concepts, such as vector spaces, distances, bases and matrix factorizations, among others. It can also be used as an example of mathematical modeling. The data are represented as vectors and matrices. For data sets of modest size, a relatively simple tool can be used and for larger data sets the need is seen to reduce the size of the problem leading to the need to introduce more sophisticated tools.