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.


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