$A\in \mathbb{C}^{n\times n}$. Set: $$ r(A) = \max_{||u||_2=1}|u^* Au| $$
Prove the following statements:
(1) $||A||_2 \leq 2 r(A)$
(2)if $A^*A=AA^*$ then $r(A)=||A||_2$
$A\in \mathbb{C}^{n\times n}$. Set: $$ r(A) = \max_{||u||_2=1}|u^* Au| $$
Prove the following statements:
(1) $||A||_2 \leq 2 r(A)$
(2)if $A^*A=AA^*$ then $r(A)=||A||_2$