Definition:Scalar Addition/Vector Space

Definition

Let $\struct {K, +_K, \times_K}$ be a field.

Let $\struct {G, +_G}$ be an abelian group.

Let $V := \struct {G, +_G, \circ}_K$ be the corresponding vector space over $K$.

The field addition operation $+_K$ on $V$ is known as scalar addition on $V$.