I am teaching a course on linear algebra and came to this theorem: every $m \times n$ matrix $A$ with rank $r$ admits a factorization $A = CR$ where $C$ is an $m \times r$ matrix and $R$ is an $r \times n$ matrix.

Then some students raised this question: are there any applications of such factorization?

As I am not specialized in algebra, I have no knowledge about this. I have looked up some literatures, and found some corollaries of this factorization about idempotent matrics. But these sound unsatisfying for people who are non-mathematicians.

So, I am aksing whether there are "real" applications? e.g., solving some mathematical modelling problems, improving computational tasks.

P.S. this does not sound like a research question. But it seems improper to ask on stackexchange.