# Definition:Scalar Field

## Definition

Let $\left({G, +_G, \circ}\right)_K$ be a vector space, where:

$\left({K, +_K, \times_K}\right)$ is a field
$\left({G, +_G}\right)$ is an abelian group $\left({G, +_G}\right)$
$\circ: K \times G \to G$ is a binary operation.

Then the field $\left({K, +_K, \times_K}\right)$ is called the scalar field of $\left({G, +_G, \circ}\right)_K$.

If the scalar field is understood, then $\left({G, +_G, \circ}\right)_K$ can be rendered $\left({G, +_G, \circ}\right)$.