 Since an elementary reflection in the form of a Householder matrix can reduce any orthogonal matrix to this constrained form, a series of such reflections can bring any orthogonal matrix to the identity; thus an orthogonal group is a reflection group.The last column can be fixed to any unit vector, and each choice gives a different copy of in ; in this way is a bundle over the unit sphere with fiber .Similarly, is a subgroup of ; and any special orthogonal matrix can be generated by Givens plane rotations using an analogous procedure.