# How to factorize the Matrix in TensorFlow? (Recommender System)

Given a user ratings matrix which is $n \times p$, where $n$ users rate $p$ movies, I already have a row matrix $n \times 10$ which characterises the user.

I ideally wanted to use the TF was method for optimisation, https://www.tensorflow.org/versions/master/api_docs/python/tf/contrib/factorization/WALSMatrixFactorization but it looks like it creates the row matrix itself.

What I need is to create the column matrix - which is $10 \times p$ (not both), containing the relationship between hidden characteristics (10) to the movies (p).

How can I do this in TF?

If R is the rating matrix, U is the user matrix and M is the movie matrix, then note that there is almost certainly no matrix M that satsifes $R = UM$. U and M are too low rank. However you should be able to find the matrix M that minimizes $|R - UM|$.
You've found an ALS solver and if you just need to solve one step and have the user matrix already, I think you just supply it as row_init and run one iteration? haven't used it, but conceptually that's all you are doing. You don't need weights either.