Definition:Vector Addition/Vector Space

Definition
Let $\struct {F, +_F, \times_F}$ be a field.

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

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

The group operation $+_G$ on $V$ is known as vector addition on $V$.

Vector Addition on Real Vector Space
The usual context for vector addition is on a real vector space or complex vector space: