Matrix completion is part of it, also determinant processes, reinforcement learning, clustering, ...

There are different methods behind recommenders. Some are content based, such as the user watched a movie with will Ferrell, show more movies with Will Ferrell. Others are based on user behavior, such as other users who watched this will Ferrell movie also watched these movies.

Edit: here is a good overview I found https://towardsdatascience.com/recommendation-systems-explained-a42fc60591ed