Unitary spaces on Clifford algebras

TL;DR

This paper introduces a Hermitian scalar product on complex Clifford algebras, leading to the construction of unitary spaces and new normal matrix representations that reflect the algebra's structure.

Contribution

It defines a Hermitian scalar product on Clifford algebras and proposes a novel construction of matrix representations considering the unitary space structure.

Findings

Defined a Hermitian scalar product depending on (p,q) signature

Constructed unitary spaces on Clifford algebras

Developed new normal matrix representations

Abstract

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.