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| | In the [[mathematics|mathematical]] study of [[transformation group]]s, the '''special affine group''' is the [[group (mathematics)|group]] of [[affine transformation]]s of a fixed [[affine space]] which preserve [[volume]]. This is the affine analogue of the [[special linear group]]. |
| | |
| | On '''R'''<sup>n</sup>, every special affine transformation has the form |
| | |
| | :<math>\mathbf{x}\mapsto A\mathbf{x}+\mathbf{b}</math> |
| | |
| | where ''A'' is an ''n''×''n'' [[matrix (mathematics)|matrix]] of [[determinant]] one, and '''b''' is a fixed vector in '''R'''<sup>n</sup>. The special affine group is a [[subgroup]] of the [[affine group]]. |
| | |
| | {{geometry-stub}} |
| | [[Category:Lie groups]] |
Latest revision as of 08:45, 18 March 2013
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. This is the affine analogue of the special linear group.
On Rn, every special affine transformation has the form
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.
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