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Say, I have calculated the singular value decomposition of a matrix $$ A = USV^T $$

Now, if I select an arbitrary number of rows of $A$, I get a sub-matrix of $A$, which I call $A_{[n]}$. I would like to calculate the singular values of $A_{[n]}$ from the singular value decomposition above. Is that possible?

Many thanks, Max

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In general, answer is no. When you select $k$ rows of $A$ arbitrarily, you are effectively multiplying $A$ with a $k \times N$ matrix $P$ whose rows are from the $n \times n$ identity matrix. Thus, $A_{[n]}=PA = PUSV^T$

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