Hybrid Complex Numbers: The Matrix Version

Hybrid Complex Numbers: The Matrix Version In this paper we review the notion of hybrid complex numbers, recently introduced to provide a comprehensive conceptual and formal framework to deal with circular, hyperbolic and dual complex. We exploit the established isomorphism between complex numbers as abstract entities and as two dimensional matrices in order to derive the associated algebraic properties. Within such a respect we derive generalized forms of Euler exponential formula and explore the usefulness and relevance of operator ordering procedure of the Wei-Norman type. We also discuss the properties of dual numbers in terms of Pauli matrices. Finally we explore generalized forms of Dirac-like factorization, emerging from the properties of these numbers. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Applied Clifford Algebras Springer Journals

Hybrid Complex Numbers: The Matrix Version

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics; Physics, general
ISSN
0188-7009
eISSN
1661-4909
D.O.I.
10.1007/s00006-018-0870-y
Publisher site
See Article on Publisher Site

Abstract

In this paper we review the notion of hybrid complex numbers, recently introduced to provide a comprehensive conceptual and formal framework to deal with circular, hyperbolic and dual complex. We exploit the established isomorphism between complex numbers as abstract entities and as two dimensional matrices in order to derive the associated algebraic properties. Within such a respect we derive generalized forms of Euler exponential formula and explore the usefulness and relevance of operator ordering procedure of the Wei-Norman type. We also discuss the properties of dual numbers in terms of Pauli matrices. Finally we explore generalized forms of Dirac-like factorization, emerging from the properties of these numbers.

Journal

Advances in Applied Clifford AlgebrasSpringer Journals

Published: Jun 4, 2018

References

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