#gershgorin

$\mathbf{M} = \begin{bmatrix} 4 & 2 \\ 2 & 100 \end{bmatrix}$ has condition number about 25. After diagonal preconditioning, $\tilde{\mathbf{M}} = \textrm{diag}^{-\frac{1}{2}}(\mathbf{M})\,\mathbf{M}\,\textrm{diag}^{-\frac{1}{2}}(\mathbf{M})$, the Gershgorin circle theorem confines every eigenvalue of $\tilde{\mathbf{M}}$ to an interval. Which upper bound on the condition number of $\tilde{\mathbf{M}}$ follows?