Singular Value Decomposition of an nxn matrix?

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The discussion revolves around the singular value decomposition (SVD) of a specific 2x2 matrix. Initially, the user expressed confusion over finding eigenvectors for the matrix A^T*A, believing none existed. However, after realizing a calculation error, the user acknowledged that A^T*A does indeed have multiple eigenvectors. The conversation highlights the importance of careful calculation in linear algebra when determining SVD. Ultimately, the user confirmed that the SVD can be successfully computed for the matrix in question.
s_j_sawyer
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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.
 
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What do you think A^T*A is? It looks to me like it has lots of eigenvectors.
 

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