Norm of Hermitian Operator

Theorem
Let $\mathbb F \in \set {\R, \C}$.

Let $\HH$ be a Hilbert space over $\mathbb F$.

Let $A : \HH \to \HH$ be a bounded Hermitian operator.

Let $\innerprod \cdot \cdot_\HH$ denote an inner product on $\HH$.

Then the norm of $A$ satisfies:


 * $\norm A = \sup \set {\size {\innerprod {A h} h_\HH}: h \in \HH, \norm h_\HH = 1}$