# Definition:Scalar Multiplication/Vector Space

## Definition

Let $\struct {G, +_G, \circ}_K$ be a vector space, where:

$\struct {K, +_K, \times_K}$ is a field
$\struct {G, +_G}$ is an abelian group.

The operation $\circ: K \times G \to G$ is called scalar multiplication.

## Also known as

Some sources refer to scalar multiplication as exterior multiplication.

## Also see

• Results about scalar multiplication can be found here.