Information loss in factorization

You may wonder how the factors with far fewer columns can summarize a larger DataFrame without loss. In fact, it doesn't — the factors we create are generally a close approximation of the data, as it is inevitable for some information to be lost. This means that predicted values might not be exact, but should be close enough to be useful.

In this exercise, you will inspect the same original pre-factorization DataFrame from the last exercise loaded as original_df, and compare it to the product of its two factors, user_matrix and item_matrix.