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.