Full-rank factorization

Am $$m\times n$$ matrix $$\mathbf A$$ of rank $$r$$ can be factored as $$\mathbf{A=BC}$$ where $$\mathbf B$$ is $$m\times r$$ and $$C$$ is $$r\times n$$. This factorization can be useful for speeding up computations, especially if $$r<<n$$. Similarly, one can do approximate full-rank factorization with SVD.