# Singular Value Decomposition

## Homework Statement

Let A be a real mxn matrix, m>=n, with singular values $$\sigma$$j.Show that the singular values of ($$\stackrel{I_{n}}{A}$$) are equal to $$\sqrt{1+\sigma_j^2}$$.

## The Attempt at a Solution

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

## The Attempt at a Solution

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Also, sorry, I'm having a hard time figuring out how to have it typeset correctly to show you guys what's going on.

HallsofIvy