\begin{definition}[Definition:Compact Linear Transformation/Normed Vector Space/Definition 2]
Let $\struct {X, \norm \cdot_X}$ and $\struct {Y, \norm \cdot_Y}$ be normed vector spaces.
Let $T : X \to Y$ be a linear transformation.
We say that $T$ is a '''compact linear transformation''' {{iff}}:
:for each bounded sequence $\sequence {x_n}_{n \mathop \in \N}$ in $X$:
::the sequence $\sequence {T x_n}_{n \mathop \in \N}$ has a subsequence convergent in $\struct {Y, \norm \cdot_Y}$.
\end{definition}