Changes

A '''vector field''' is a [[vector]] ''function'' that assigns a vector to each point in a region.

A '''vector field''' is a [[vector]] ''function'' that assigns a vector to each point in a region. So, if <math>S</math> is a subset of the <math>\mathbb{R}^n</math>, then a vector field can be seen as the function <math>\vec{V}: S \rightarrow \mathbb{R}^n</math>, which maps an n-dimensional vector <math>\vec{x}=(x_1, x_2, \dots, x_n) \in \mathbb{R}^n</math> to each point <math>\vec{p} \in S</math>:

 

 

This is contrasted with a [[scalar field]] that merely assigns a scalar value to each point.

This is contrasted with a [[scalar field]] that merely assigns a scalar value to each point.