implicit recommendation system

I want to develop recommendation system model. I have 900k users and 20k items and their interaction (which items was purchased by user). when I try to create matrix with 900k X 20k dimension, I get memory error (matrix is too big). I wonder, if I need different form of matrix (e.g. sparse matrix) and how can I preprocess data for implicit rating: should I binarize it with getting 1 to purchased items and 0 otherwise?

I appreciate every useful materials regarding this topics.

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It would be 72Gb

Sparse matrix would seem very necessary