\begin{definition}[Definition:Norm/Bounded Linear Transformation/Definition 3]
Let $\HH$ and $\KK$ be Hilbert spaces.
Let $A: \HH \to \KK$ be a bounded linear transformation.
The '''norm''' of $A$ is the real number defined and denoted as:
:$\norm A = \sup \set {\norm {A h}_\KK: \norm h_\HH = 1}$
{{explain|What are $\norm {A h}_\KK$ and $\norm h_\HH$?}}
\end{definition}