Universal Similarity Factorization Equalities over Real Clifford Algebras

TL;DR

This paper establishes universal similarity factorization equalities for real Clifford algebras, enabling explicit matrix representations over real, complex, and quaternion fields, which advances algebraic understanding and computational applications.

Contribution

It introduces new universal similarity factorization equalities for real Clifford algebras, facilitating explicit matrix representations across different fields.

Findings

Universal similarity equalities are established for ${ m R}_{p,q}$.

Explicit matrix representations over various fields are derived.

The results unify and extend previous algebraic representations.

Abstract

A variety of universal similarity factorization equalities over real Clifford algebras ${\cal R}_{p,q}$ are established. On the basis of these equalities, real, complex and quaternion matrix representations of elements in ${\cal R}_{p,q}$ can be explicitly determined.