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Math Help - Condition number and the SVD

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    Member Mollier's Avatar
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    Condition number and the SVD

    Hi,

    problem;
    Let A be an m-by-n matrix of rank n.
    Evaluate the condition number of,

    M = \begin{pmatrix} <br />
  I     & A\\ <br />
  A^* & 0 <br />
\end{pmatrix}

    I know that the condition number of M is,

    k(A) = \frac{\sigma_{max}(M)}{\sigma_{min}(M)} where the \sigma 's are singular values.

    If I let M = U\Sigma V^* and try to find the singular values of M by somehow using A it leads me to,

    \Sigma = U^*\begin{pmatrix} <br />
  I     & A\\ <br />
  A^* & 0 <br />
\end{pmatrix}V.

    I've tried some wierd stuff from here, but it does not lead anywhere.

    Any hints?
    Thanks
    Last edited by Mollier; April 16th 2011 at 11:09 PM.
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