# Vector space

Submitted by Isoscel on Fri, 11/30/2007 - 19:44.

Here is the definition of a vector space over a field .

Let be a field and (,+) a commutative group.

such as

such as

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

,