Conservative Vector Field

Definition: Gradient Field

A real vector field $\mathbf{v}:\mathcal{D}\subseteq {\mathbb{R}}^n\to {\mathbb{R}}^n$ is conservative iff there exists a real scalar field $f:D\to \mathbb{R}$ whose gradient is $\mathbf{v}$.

$$\nabla f=\mathbf{v}$$

NOTE

Conservative vector fields are also known as gradient fields.