\begin{definition}[Definition:Normed Vector Space]
Let $\struct {K, +, \circ}$ be a normed division ring.
Let $V$ be a vector space over $K$.
Let $\norm {\,\cdot\,}$ be a norm on $V$.
Then $\struct {V, \norm {\,\cdot\,} }$ is a '''normed vector space'''.
\end{definition}