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## Homework Statement

Let A be a real mxn matrix, m>=n, with singular values [tex]\sigma[/tex]

_{j}.Show that the singular values of ([tex]\stackrel{I_{n}}{A}[/tex]) are equal to [tex]\sqrt{1+\sigma_j^2}[/tex].

## Homework Equations

## The Attempt at a Solution

I know that an SVD for A is A = U([tex]\stackrel{\Sigma}{0}[/tex])v^T and so, the singular values of A are [tex]\sigma_j[/tex]. I have no idea how to break this down. I assume I want to look at an SVD for ([tex]\stackrel{I_n}{A}[/tex]), but I don't know how to figure out that the singular values would be [tex]\sqrt{1+\sigma_j^2}[/tex]. Does anyone have any ideas? Thanks so much.

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