Here is the definition of a vector space over a field .
Let be a field and (,+) a commutative group.
Let * be a binary operation such as
Then is called a vector space over field or simply a -vector space.
Morphism of Vector Space
Let and two -vector spaces.
A function is a morphism of -vector spaces if
Subspace of a vector space
Let be a -vector space. A subset is called a vector subspace of if