\begin{definition}[Definition:Angle Between Vectors in Inner Product Space]
Let $\struct {V, \innerprod \cdot \cdot}$ be an inner product space.
Let $v,w \in V$ be such that $\size v, \size w \ne 0$, where $\size {\, \cdot \,}$ denotes the inner product norm.
Then the real number $\theta \in \closedint 0 \pi$ is called the '''angle (between $v$ and $w$)''' {{iff}}:
:$\map \cos \theta = \dfrac {\innerprod v w} {\size v \size w}$
\end{definition}