\begin{definition}[Definition:Del Operator]
Let $\mathbf V$ be a vector space of $n$ dimensions.
Let $\tuple {\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n}$ be the standard ordered basis of $\mathbf V$.
The '''del operator''' is a unary operator on $\mathbf V$ defined as:
:$\nabla := \ds \sum_{k \mathop = 1}^n \mathbf e_k \dfrac \partial {\partial x_k}$
where $\mathbf v = \ds \sum_{k \mathop = 0}^n x_k \mathbf e_k$ is an arbitrary vector of $\mathbf V$.
\end{definition}