Singular Value Decomposition of an nxn matrix?

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SUMMARY

The discussion centers on the singular value decomposition (SVD) of a 2x2 matrix, specifically the matrix [[1, 1], [-1, 1]]. Initially, the user encountered issues finding eigenvectors of the matrix A^T*A, mistakenly believing there were none. Upon reevaluation, the user corrected their calculations and acknowledged the presence of multiple eigenvectors in A^T*A. This highlights the importance of accurate computation in linear algebra.

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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.
 
Last edited:
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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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