# Singular Value Decomposition

1. Feb 25, 2009

### azdang

1. The problem statement, all variables and given/known data
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 $$\sqrt{1+\sigma_j^2}$$.

2. Relevant equations

3. 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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: Feb 25, 2009
2. Feb 25, 2009

### azdang

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

3. Feb 25, 2009

### HallsofIvy

Staff Emeritus
Don't use the html tags and inside LaTex. Use _ for subscripts and ^ for superscripts.

4. Feb 25, 2009

### azdang

Oh wow, thank you so much. It looks great.