Vector field

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

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

Formulation in Set Theory

If Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S} is a subset of the $\mathbb {R} ^{n}$, then a vector field can be seen as the function ${\vec {V}}:S\rightarrow \mathbb {R} ^{n}$, which maps an n-dimensional positional vector Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{x}=(x_1, x_2, \dots, x_n) \in \mathbb{R}^n} to each point Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{p} \in S} :

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{V}(\vec{p}) = \vec{x}}