The spin group Spin(V) is defined to be the subgroup of Cleven(V) consisting of multivectors R such that  That is, it consists of multivectors that can be written as a product of an even number of unit vectors.
Spin(V), the subgroup within Cleven(V), includes multivectors R that satisfy . Such multivectors are formed by multiplying an even number of unit vectors together, reflecting their role in this group.