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.

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

Let to be a basis of as an vector space.

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

This is just the standard 3-dimensional vector space over the real numbers.

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.

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

A vector space is an external ring over a field.

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

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.

But these forms the basis of a vector space in which every form has the right properties.

It is often possible to supply a norm for a given vector space in more than one way.

Let be a field and a vector space over .

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

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

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

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

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

The norm is a continuous function on its vector space.

Elements of the vector space can also be analyzed statistically.

This also shows that the size of any finite vector space is a prime power.