How to show that for $A \in M_n(\mathbb{R})$, $||A||_2 \leq ||A||_{F}$? That is, the induced $l_2$ norm on matrices is bounded by the Hilbert-Schmidt norm?
Recall that $||A||_2 = \sup_{v \neq 0}\frac{||Av||_2}{||v||_2}$, and $||A||_F = (\sum_{i=1}^n\sum_{j=1}^n|a_{ij}|^2)^{\frac{1}{2}}$.
Thanks in advance.