Hybrid Complex Numbers: The Matrix Version

G. Dattoli, S. Licciardi, R.M. Pidatella, E. Sabia

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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.
Original languageEnglish
Article number58
Pages (from-to)-
JournalAdvances in Applied Clifford Algebras
Issue number3
Publication statusPublished - 1 Jul 2018
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

Dattoli, G., Licciardi, S., Pidatella, R. M., & Sabia, E. (2018). Hybrid Complex Numbers: The Matrix Version. Advances in Applied Clifford Algebras, 28(3), -. [58]. https://doi.org/10.1007/s00006-018-0870-y