\begin{definition}[Definition:Norm/Bounded Linear Functional/Normed Vector Space/Definition 2]
Let $\mathbb F$ be a subfield of $\C$. 
Let $\struct {V, \norm \cdot}$ be a normed vector space over $\mathbb F$ with $V \ne \set 0$.
Let $L : V \to \mathbb F$ be a bounded linear functional.
The '''norm''' of $L$ is defined as the supremum:
:$\norm L = \sup \set {\size {L v}: \norm v = 1}$
Category:Definitions/Norm on Bounded Linear Functional
\end{definition}