Definition:Del Operator

Definition
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:


 * $\nabla := \displaystyle \sum_{k \mathop = 1}^n \mathbf e_k \dfrac \partial {\partial x_k}$

where $\mathbf v = \displaystyle \sum_{k \mathop = 0}^n x_k \mathbf e_k$ is an arbitrary vector of $\mathbf V$.

Also known as
The del operator is often seen referred to as nabla, but the latter term is technically to be applied to the $\nabla$ symbol itself.

Also see

 * Definition:Gradient Operator
 * Definition:Divergence Operator
 * Definition:Curl Operator