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I have a symmetric matrix, $\hat{A}, $which is an estimator of another true symmetric matrix, $A$. I would like to estimate the column space of $A$. I know I can do QR-Algorithm or use spectral decomposition to find non-zero eigenvectors of $\hat{A}$ and use these vectors to generate the column space.

I was wondering when QR give a better estimator than the spectral decomposition method.

bankrip
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  • What is meant by estimating the column space of $A$? There are many different techniques that are used to measure this. But if you're trying to minimize $| \hat{A} - A |_2$ then the SVD is optimal. – Christopher A. Wong Feb 20 '14 at 03:44
  • Thanks. I actually want to minimize the norm of $P_{\hat{A}} - P_{A}$, where $P_{A}$ is the orthogonal projector to column space of $A$. I know that SVD is optimal in general, but I believe there are cases it would be outperformed QR. I am trying to find examples when SVD is worse than QR. – bankrip Feb 20 '14 at 03:54

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