Definition:Vector

Vector (Module)
Let $\struct {G, +_G, \circ}_R$ be a module, where:


 * $\struct {G, +_G}$ is an abelian group


 * $\struct {R, +_R, \times_R}$ is the scalar ring of $\struct {G, +_G, \circ}_R$.

Vector (Linear Algebra)
Let $V = \struct {G, +_G, \circ}_K$ be a vector space over $K$, where:


 * $\struct {G, +_G}$ is an abelian group


 * $\struct {K, +_K, \times_K}$ is the scalar field of $V$.

Also see

 * Definition:Directed Line Segment: a vector whose vector space is a Euclidean space.


 * Definition:Vector Field