\begin{definition}[Definition:Norm/Bounded Linear Transformation/Definition 1]
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:
:$\norm A = \sup \set {\norm {A h}_\KK: \norm h_\HH \le 1}$
{{explain|So what are $\norm {A h}_\KK$ and $\norm h_\HH$? The norm of something else?}}
\end{definition}