Perhaps the most important example of a vector space is the following.

Let to be a basis of as an vector space.

Then, the complex numbers themselves clearly form a vector space.

Here one is working with a vector space over the complex numbers.

Let C be a set in a real or complex vector space.

It is true that every vector space has a basis.

One must also consider the type of field over which the vector space is defined.

Let V be any vector space over the complex numbers.

The Lie group acts on the vector space in a natural way.

See vector space for the definitions of terms used on this page.

A vector space is an external ring over a field.

As it stands, V is only a real vector space.

Let S be a vector space over the real numbers, or, more generally, some ordered field.

The real numbers with the usual order is an ordered vector space.

Suppose is a vector space over a field of characteristic 0.

More formally, a vector space is a special combination of a group and a field.

Therefore is a vector space over Z, the field with two elements.

Let be a field and a vector space over .

A vector space over the complex numbers of dimension 2n r.

The real number vector space 'R'3 has as a spanning set.

This means that all the properties of the vector space are satisfied.

Arrays take Vector space in the number of elements they hold.

The norm is a continuous function on its vector space.

There is an analogy with the theory of vector space dimensions.

Elements of the vector space can also be analyzed statistically.