Definition:Scalar Multiplication/Vector Space

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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.