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.
There is a unique antiautomorphism of Cl(V) which restricts to the identity on V: this is called the transpose, and the transpose of any multivector a is denoted by .