affine space

There are several different systems of axioms for affine space.

Let be a Euclidean affine space of dimension at least 2.

An affine space of positive dimension is not complete.

In the second case, the tangent space is that line, considered as affine space.

For example, is a meromorphic function on the two-dimensional complex affine space.

Similarly, starting from an affine space A, every class of parallel lines can be associated with a point at infinity.

An underlying set with an affine structure is an affine space.

"Is parallel to" on the set of subspaces of an affine space.

See affine space for more detailed information about computing the location of the plane at infinity '.

Conversely, any vector space 'V' is an affine space over itself.

This is a surface in affine space.

Every linear space is also an affine space.

In affine space, the union of a line and a point not on the line is not equidimensional.

The intersection of the rational normal curve with an affine space is called the moment curve.

More generally, a half-space is either of the two parts into which a hyperplane divides an affine space.

They divided the 219 affine space groups into reducible and irreducible groups.

More precisely, an affine space is a set with a free transitive vector space action.

The formal mathematical term is an affine space (in this case an affine line).

Informally, an affine space is a vector space without a fixed choice of origin.

In an affine space such as the Euclidean plane a similar statement is true, but only if one lists various exceptions involving parallel lines.

Affine space is a geometry in this sense, and is equipped with a flat Cartan connection.

For any isometry group in Euclidean space the set of fixed points is either empty or an affine space.

For example, the de Casteljau algorithm may be used to split a curve in affine space; this does not work on a sphere.

Roughly, affine spaces are vector spaces whose origin is not specified.

The choice of the origin is arbitrary: any other point may be chosen, as the representation is of an affine space.