I have question on how to use the basic form of SVD to do recommendation. I read a lot online and most of them are talking about what svd is, how it factorize the matrix, but not much about how to actually do a recommendation.

After we get all the latent factors, if we just using all are them, aren’t we going to get the original matrix exactly? What did we predict exactly? If there is missing value, how does the basic SVD works? I know there are some variation of SVD using SGD and simply ignore missing entries, but I am interested in the basic form since a lot of people talking about SVD but I can’t really find an good article discuss this, as it is overwhelmed by collaborative filtering.