Singular Value Decomposition of an nxn matrix?

[s_j_sawyer]

I was just wondering if it was possible to find the singular value decomposition of an nxn matrix such as

1 1
-1 1

I tried this but then when finding the eigenvectors of A^T*A I found there were none (non-trivial anyhow).

So, is this not possible?

EDIT:

How embarrassing I made an error in my calculations. Sorry, it's all good now.

 

[Dick]

What do you think A^T*A is? It looks to me like it has lots of eigenvectors.