Abstract
In this study, we investigate the matrices over the new extension of the real numbers in four dimensional space E2^4 called the hybrid numbers. Since the hybrid multiplication is noncommutative, this leads to finding a linear transformation 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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