1. ## Norm inequality

Hi,

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

I've tried a few things (with no luck), such that first trying to show that $\|A\|_{\infty}\geq \| |A| \|_2$,
and then use the fact that $\sqrt{n}\|A\|_2\geq \|A\|_{\infty}$.

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

Thanks.

2. ## Re: Norm inequality

I don't know what the norm notations refer, but did you try to use Cauchy-Schwarz inequality?