\begin{definition}[Definition:Inner Product Norm]
Let $\Bbb F$ be a subfield of $\C$. 
Let $\struct {V, \innerprod \cdot \cdot}$ be an inner product space over $\Bbb F$.
Then the '''inner product norm''' on $V$ is the mapping $\norm \cdot : V \to \R_{\ge 0}$ given by:
:$\norm x = \sqrt {\innerprod x x}$
for each $x \in V$.
\end{definition}