The dual quaternion matrices

In this study, firstly, it was shown that the set of dual quaternion matrices Mn(HD) is a n2 -dimensional module and 4 - dimensional module over the dual quaternion ring HD and the real matrix ring Mn(R), respectively, where D is the set of dual numbers. Besides, properties such as addition, multiplication, conjugate, transpose, conjugate transpose, inverse, power and trace were examined on the set of the dual quaternion matrices. The obtained results were compared with properties of the dual quaternions. Moreover, real matrix representations of the dual quaternion matrices were introduced and their properties were described. These were applied to find determinant and inverse of the dual quaternion matrices. Also, different types of determinant and inverse of the dual quaternion matrices were defined. Finally, examples of obtained results were also solved by Matlab.