What are vector spaces?
Let (F,+,.) be a field. The element of F will be called scalars. Let V be a non-empty set whose elements will be called vector. Then V is a vector space over the field F.
If an internal composition in V called the addition of vectors and denoted by'+'.Also for this composition Vis an abelian group.
An external composition in V over F called scalar multiplication and denoted by multiplicatively so that ax⋿V for all a⋿ F and for all 𝞪⋿V(V is close to scalar multiplication)