lower bound for the condition number
Solution 1:
Take $C=\begin{pmatrix}0&0&0\\0&-\alpha&-\alpha\\0&-\alpha&-\alpha\end{pmatrix}$. If $\alpha$ is small, then $cond_{\infty}(A)\geq l_{\alpha}=\dfrac{3}{2|\alpha|}$.
lower bound for the condition number
Solution 1:
Take $C=\begin{pmatrix}0&0&0\\0&-\alpha&-\alpha\\0&-\alpha&-\alpha\end{pmatrix}$. If $\alpha$ is small, then $cond_{\infty}(A)\geq l_{\alpha}=\dfrac{3}{2|\alpha|}$.