jum Journal of Universal Mathematics 2618-5660 2618-5660 Gökhan ÇUVALCIOĞLU 10.33773/jum.1332081 Algebraic and Differential Geometry Real and Complex Functions (Incl. Several Variables) Cebirsel ve Diferansiyel Geometri Reel ve Kompleks Fonksiyonlar MATRICES OF HYBRID NUMBERS https://orcid.org/0000-0002-2809-8324 Ramis Çağla NEVSEHIR HACI BEKTAS VELI UNIVERSITY https://orcid.org/0000-0001-6369-540X Yazlik Yasin NEVSEHIR HACI BEKTAS VELI UNIVERSITY 10 15 2023 6 3-Supplement 1 15 07 24 2023 10 08 2023 Copyright © 2018, Journal of Universal Mathematics 2018 Journal of Universal Mathematics

In this study, we investigate the matrices over the new extension of the real numbers in four dimensional space E2^4called the hybrid numbers. Since the hybrid multiplication is noncommutative, this leads to finding a lineartransformation on the complex field. Thus we characterize the hybrid matrices and examine their algebraic properties with respect to their complex adjoint matrices. Moreover, we define the co-determinant of hybrid matrices which plays an important role to construct the Lie groups.

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