\begin{definition}[Definition:Dot Product]
Let $\mathbf a$ and $\mathbf b$ be vectors in a vector space $\mathbf V$ of $n$ dimensions:
:$\mathbf a = \ds \sum_{k \mathop = 1}^n a_k \mathbf e_k$
:$\mathbf b = \ds \sum_{k \mathop = 1}^n b_k \mathbf e_k$
where $\tuple {\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n}$ is the standard ordered basis of $\mathbf V$.
\end{definition}