# Homework Help: Show Matrix 2-Norm Greater than Matrix Inf-Norm

1. Sep 8, 2010

### blabbate

1. The problem statement, all variables and given/known data
Show $$\sup _{x \neq 0}\|Ax\|_\infty/\|x\|_\infty\leq\|Ax\|_2/\|x\|_\infty$$

2. Relevant equations
See above.

3. The attempt at a solution
I'm not looking for a full solution, just a push in the right direction. I've tried breaking out the numerators such that $$\|Ax\|\leq\|A\|\|x\|$$ on both sides and multiplying through, as well as trying to use $$\|x\|_2\geq\|x\|_\infty$$ and substituting to get a suitable inequality, but no luck.