Vector space (Personal website)

Vector space

The set

$V$ defined over the field $F$

that contains the zero vector, so

 $\vec{0} \in V,$

in conjunction with the vector addition operation

 $\forall \vec{u}, \vec{v} \in V : \vec{u} + \vec{v} \in V$

that satisfies all properties listed here

 $\forall a \in F, \forall \vec{v} \in V : a \vec{v} \in V$

that satisfies all properties listed here.

which is the one and only

link between vector addition and scalar multiplication