Dual Quaternion Matrices and MATLAB Applications - Nalbant, Kemal Gokhan; Yuce, Salim (PRAIRIE VIEW A & M UNIV, DEPT MATHEMATICS, 2024)
There are many studies in the literature on real quaternions and real quaternion matrices. There are few studies in the literature on dual quaternions. Definitions of the matrices of dual quaternions used in this study will be given. The originality of our research, the set of dual quaternion matrix we studied, will be defined for the first time in this study, and its properties will be given. Moreover, this study is critical because it is an applied study related to dual quaternion matrices. It will be easier to solve examples with large matrix sizes with MATLAB. People who use different programs can also write applications inspired by them. In this work, the set of dual quaternion matrices is examined. Among the dual quaternion matrices, additional features such as addition, multiplication, inverse, transpose, conjugate, power, and trace are explored. In addition, real matrix representations of dual quaternion matrices and their characteristics were developed. These were utilized to determine the dual quaternion matrices' determinants and inverses. In addition, many types of determinants and inverses of dual quaternion matrices were created, and MATLAB applications were developed to facilitate the solution of cases utilizing these techniques. Finally, the results and methodologies were compared to the actual quaternion matrix characteristics.
Keywords: Quaternions; Dual quaternions; Dual quaternion matrices; Real matrix representa- tion; MATLAB applications; Inverse; Power; Determinant; Mathematics