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Given a Matrix $A$ where the SVD would be $$A= U \Sigma V^t$$

Where $\Sigma$ is a diagonal matrix with its singular values

Assuming that I only had the $\Sigma$ values and I don't have the $U$ and $V$ values. Let's say $\sigma_i$ corresponds to the columns of the $\Sigma$ matrix of singular values.

Is it possible to know which column in the original matrix $A$ does the $\sigma_i$ correspond to? If so how can I do it?

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