# Definitions > [!NOTE] Definition (Vector Field) > A **vector field on subset of real n-space** is a [[Function|function]] $f: U\subset \mathbb{R}^{n}\to \mathbb{R}^{n},$ where $\mathbb{R}^{n}$ > denotes the [[Real n-Space|real n-space]] of dimension $n\in\mathbb{N}.$