Definition:Vector Addition

Definition

Vector Addition on Module

Let $\struct {R, +_R, \times_R}$ be a ring.

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

Let $M := \struct {G, +_G, \circ}_R$ be the corresponding module over $R$ (either a left module or a right module).

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

Vector Addition on Vector Space

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 $V$.

Also known as

Vector addition is also known as composition.

Also see

• Definition:Vector Sum

• Results about vector addition can be found here.