Hi,

problem;

Let $\displaystyle A$ be an m-by-n matrix of rank $\displaystyle n$.

Evaluate the condition number of,

$\displaystyle M = \begin{pmatrix}

I & A\\

A^* & 0

\end{pmatrix}$

I know that the condition number of $\displaystyle M$ is,

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

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

$\displaystyle \Sigma = U^*\begin{pmatrix}

I & A\\

A^* & 0

\end{pmatrix}V$.

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

Any hints?

Thanks