Hi,

I need to show that $\displaystyle \| |A| \|_2 \leq \sqrt{n} \|A\|_2$ where $\displaystyle A$ is $\displaystyle m\times n$. THe $\displaystyle |A|$ notation means we take the absolute value of all elements of $\displaystyle A$.

I've tried a few things (with no luck), such that first trying to show that $\displaystyle \|A\|_{\infty}\geq \| |A| \|_2$,

and then use the fact that $\displaystyle \sqrt{n}\|A\|_2\geq \|A\|_{\infty}$.

Would be great if someone could give me a hint or two.

Thanks.