\begin{definition}[Definition:Bounded Linear Transformation/Normed Vector Space]
Let $\struct {V, \norm \cdot_V}$ and $\struct {U, \norm \cdot_U}$ be normed vector spaces.
Let $A : V \to U$ be a linear transformation.
We say that $A$ is a '''bounded linear transformation''' {{iff}}:
:there exists $c > 0$ such that $\norm {A v}_U \le c \norm v_V$ for each $v \in V$.
\end{definition}