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So - I know if you perform SVD to a matrix $X$, you can then use Echkart Young theorem to get the best rank $r$ approximation $\overline{X}$ to $X$ possible. Since the resultant ${\overline{X}}$ will be of a lower rank, that means some of the rows will be linear combinations of the others, and so rather than store all of ${\overline{X}}$ you could simply store some of the rows of ${\overline{X}}$, with the combinations required to achieve the other rows. So it's a sort of "compression" technique.

Does this make sense/would it be sensible to do? I know there are clearly going to be better compression techniques out there, I'm just asking if in theory this would indeed provide a sort of lossy compression. Thanks!

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