A Generalization of complex, dual and hyperbolic quaternions: hybrid quaternions
Dagdeviren A.
2023University of Nis
Filomat
2023#37Issue 258441 - 8454 pp.
Hybrid numbers are a new non-commutative number system which is a generalization of the complex (i2 = −1), dual (ε2 = 0), and hyperbolic numbers (h2 = 1). In this article, firstly we define a new quaternion system called hybrid quaternions by taking the coefficients of real quaternions as hybrid numbers. This new quaternion system is a combination of complex quaternions (biquaternions), hyperbolic (perplex) quaternions, and dual quaternions, and it can be viewed as a generalization of these quaternion systems. Then, we present the basic properties of hybrid quaternions including fundamental operations, conjugates, inner product, vector product, and norm. Finally, we give a schematic representation of numbers and quaternions.
Complex quaternions , Dual quaternions , Hyperbolic quaternions , Real quaternions
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Department of Computer Engineering, Faculty of Engineering, Khoja Akhmet Yassawi International Kazak-Turkish University, Kazakhstan
Department of Computer Engineering
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