\begin{definition}[Definition:Norm/Bounded Linear Functional/Inner Product Space/Definition 4]
Let $\mathbb F$ be a subfield of $\C$.
Let $\struct {V, \innerprod \cdot \cdot}$ be an inner product space over $\mathbb F$ with $V \ne \set 0$.
Let $L : V \to \mathbb F$ be a bounded linear functional.
Let $\norm \cdot$ be the inner product norm for $\struct {V, \innerprod \cdot \cdot}$.
The '''norm''' of $L$ is the infimum:
:$\norm L = \inf \set {c > 0: \forall v \in V : \size {L v} \le c \norm v}$
As $L$ is bounded, it is assured that $\norm L < \infty$.
\end{definition}