In mathematics, the **affine group** or **general affine group** of any affine space over a field *K* is the group of all invertible affine transformations from the space into itself.

It is a Lie group if *K* is the real or complex field or quaternions.

Read more about Affine Group: Matrix Representation, Planar Affine Group

### Other articles related to "affine group, affine, group, groups":

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... The PoincarĂ© group is the affine group of the Lorentz group. ...

**Affine Group**s - PoincarĂ© Group... The PoincarĂ© group is the affine group of the Lorentz group. ...

Affine Representation

... An

... An

**affine**representation of a topological (Lie)**group**G on an**affine**space A is a continuous (smooth)**group**homomorphism from G to the automorphism**group**of A, the**affine group**Aff(A) ... Similarly, an**affine**representation of a Lie algebra g on A is a Lie algebra homomorphism from g to the Lie algebra aff(A) of the**affine group**of A ... An example is the action of the Euclidean**group**E(n) upon the Euclidean space En ...Euclidean Group - Overview - Relation To The

... The Euclidean

**Affine Group**... The Euclidean

**group**E(n) is a subgroup of the**affine group**for n dimensions, and in such a way as to respect the semidirect product structure of both**groups**... real column vector of size n or by a single square matrix of size n + 1, as explained for the**affine group**... we read off from this that Euclidean geometry, the geometry of the Euclidean**group**of symmetries, is therefore a specialisation of**affine**geometry ...Group Scheme - Basic Properties

... over a field, one often can analyze a

... over a field, one often can analyze a

**group**scheme by treating it as an extension of**group**schemes with distinguished properties ... Any**group**scheme G of finite type is an extension of the connected component of the identity (i.e ... the maximal connected subgroup scheme) by a constant**group**scheme ...### Famous quotes containing the word group:

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