This is a practice question for an exam, which im not able to figure out.
Show that these two definitions of norms are equivalent: $||A||_2=\max_{||v||_2=1}||Av||_2$ and $||A||_2=\max_{x,y} \frac{x^tAy}{||x||_2||y||_2}$.
Can someone help me in showing their equivalence
In the second formulation, fix $x$ and find the $y$ that maximizes the expression.