### Truncated SVD

Hi!
I'm a little confused about the dimensions of the matrices.
1) The Uk matrix has size DK, then the Uk^TU matrix must have size KD and after multiplying with the S matrix, the resulting matrix has size KN. But the Sk matrix has size D*N... And how was the last equality obtained - the matrix Uk replaced by the matrix U?

2) Also, these 2 formulas seem contradictory to me. They are the same except for U and Uk.

3) Why multiplication by matrix U gives compression? Isn't Uk the compression matrix?

Thank you in advance!

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