Category:Norm of Hermitian Operator

This category contains pages concerning Norm of Hermitian Operator:

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

Let $\struct {\HH, \innerprod \cdot \cdot_\HH}$ be a Hilbert space over $\mathbb F$.

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

Let $\norm \cdot_\HH$ be the inner product norm on $\HH$.

Then the norm of $A$ satisfies:

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