Each of these groups has a subgroup of orientation-preserving or positive affine transformations: those where the determinant of is positive. In the last case this is in 3D the group of rigid transformations (proper rotations and pure translations).
Each of these groups has a subgroup of orientation-preserving or positive affine transformations: those where the determinant of is positive. In the last case this is in 3D the group of rigid transformations (proper rotations and pure translations).