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.

Hybrid Complex Numbers: The Matrix Version

Licciardi, S.;Pidatella, R. M.;
2018-01-01

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.
2018
Hybrid complex numbers; Matrix algebra; Quaternions; Operator ordering; Clifford numbers; Dual numbers
File in questo prodotto:
File Dimensione Formato  
Hybrid Complex numbers.pdf

solo gestori archivio

Tipologia: Versione Editoriale (PDF)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 196.63 kB
Formato Adobe PDF
196.63 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/359285
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 8
social impact