  For the complex Clifford algebra Cl(p,q) of dimension n=p+q we define a
Hermitian scalar product. This scalar product depends on the signature (p,q) of
Clifford algebra. So, we arrive at unitary spaces on Clifford algebras. With
the aid of Hermitian idempotents we suggest a new construction of, so called,
normal matrix representations of Clifford algebra elements. These
representations take into account the structure of unitary space on Clifford
algebra.
