Category:Definitions/Del Operator

This category contains definitions related to the $\nabla$ operator.
Related results can be found in Category: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 $\mathbf V$.