\begin{definition}[Definition:Norm/Bounded Linear Transformation/Definition 2]
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:
:$\norm A = \sup \set {\dfrac {\norm {A h}_\KK} {\norm h_\HH}: h \in \HH, h \ne \mathbf 0_\HH}$
{{explain|So what are $\norm {A h}_\KK$ and $\norm h_\HH$? The norm of something else?}}
\end{definition}