Special affine group

Special affine group

In the mathematical study of transformation groups, the special affine group is the group of affine transformations of a fixed affine space which preserve volume.

On Rn, every special affine transformation has the form

:mathbf{x}mapsto Amathbf{x}+mathbf{b}

where "A" is an "n"×"n" matrix of determinant one, and b is a fixed vector in Rn. The special affine group is a subgroup of the affine group.


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Affine group — 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… …   Wikipedia

  • Affine — may refer to:*Affine cipher, a special case of the more general substitution cipher *Affine combination, a certain kind of constrained linear combination *Affine connection, a connection on the tangent bundle of a differentiable manifold *Affine… …   Wikipedia

  • Affine curvature — This article is about the curvature of affine plane curves, not to be confused with the curvature of an affine connection. Special affine curvature, also known as the equi affine curvature or affine curvature, is a particular type of curvature… …   Wikipedia

  • Affine geometry of curves — In the mathematical field of differential geometry, the affine geometry of curves is the study of curves in an affine space, and specifically the properties of such curves which are invariant under the special affine group In the classical… …   Wikipedia

  • General linear group — Group theory Group theory …   Wikipedia

  • Affine connection — An affine connection on the sphere rolls the affine tangent plane from one point to another. As it does so, the point of contact traces out a curve in the plane: the development. In the branch of mathematics called differential geometry, an… …   Wikipedia

  • Group representation — In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group… …   Wikipedia

  • Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia

  • Lorentz group — Group theory Group theory …   Wikipedia

  • Mathieu group — Group theory Group theory …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”