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In this study, the hybrid-hyperbolic numbers are introduced. This number system is a more general form of the hybrid number system, which is an interesting number system, as well as a number system that includes multicomponent number systems (i.e., complex-hyperbolic, dual-hyperbolic and bihyperbolic numbers). In this paper, we give algebraic properties of hybrid-hyperbolic numbers. In addition, 2 × 2 and 4 × 4 hyperbolic matrix representations of hybrid-hyperbolic numbers are given and some properties of them are examined.

Multicomponent hybrid numbers: On algebraic properties and matrix representations of hybrid-hyperbolic numbers