Many computer-based services use recommender systems that predict our preferences based on our degree of satisfaction with the past selections. One of the most efficient techniques making recommender systems successful is matrix factorization. While this technique works well, until now, there was no general explanation of why it works. In this paper, we provide such an explanation. 1 Formulation of the Problem Recommender systems. Many computer-based services aim at making the customers happier. For example, platforms like amazon.com that help us buy things not only allow us to buy what we want, they also advise us about we may be interested in looking at. The system comes up with this advice based on our previous pattern of purchases and on how satisfied we were with these purchases. For example, platforms like Netflix not only allow you to watch movies, they also use our previous selections to help the customer by providing advice on what other movies this particular customer will want to see. To make such recommendations, for each customer i, the system uses the ratings rij that different customers made for different objects j. Based on the