Divergence

Given a vector field \(\mathbf{f} : \mathbb{R}^n \rightarrow \mathbb{R}^m\), the divergence operator is defined as \[ \nabla \cdot \mathbf{f} = (\mathbf{e}_i \partial_i) \cdot (\mathbf{e)_j \mathbf{f}_j) = \frac{\partial \mathbf{f}_i}{\partial x_i}\] Where the above uses the Einstein summation convention.