Unitary spaces on Clifford algebras

In this thesis, unitary spaces on complex Clifford algebras Cl(p, q) of dimension n = p + q are studied. First of all, the basic de nitions and theorems about the Clifford algebra, real and complex Clifford algebra are discussed. Hermitian scalar product on Cl(p, q) is defined. Some properties provided by Hermitian scalar product are examined. This scalar product depends on the signature (p, q) of complex Clifford algebra. The Hermitian idempotent concept is defined on Cl(p, q) and a method is constructed to obtain normal matrix representations of the complex Clifford algebra with the aid of Hermitian idempotents. By using these normal representations the structure of unitary spaces on complex Clifford algebra is examined.