Si, K.-W.; Wang, Q.-W. The General Solution to a Classical Matrix Equation AXB = C over the Dual Split Quaternion Algebra. Symmetry2024, 16, 491.
Si, K.-W.; Wang, Q.-W. The General Solution to a Classical Matrix Equation AXB = C over the Dual Split Quaternion Algebra. Symmetry 2024, 16, 491.
Si, K.-W.; Wang, Q.-W. The General Solution to a Classical Matrix Equation AXB = C over the Dual Split Quaternion Algebra. Symmetry2024, 16, 491.
Si, K.-W.; Wang, Q.-W. The General Solution to a Classical Matrix Equation AXB = C over the Dual Split Quaternion Algebra. Symmetry 2024, 16, 491.
Abstract
In this paper, we establish the necessary and sufficient conditions for solving a dual split quaternion matrix equation AXB=C, and present the general solution expression when solvability is achieved. As an application, we delve into the necessary and sufficient condition for the existence of Hermitian solution to this equation by using a newly defined real representation method. Furthermore, we obtain the solutions for the dual split quaternion matrix equations AX=C and XB=C. Finally, we provide a numerical example to demonstrate the findings of this paper.
Keywords
dual split quaternion; real representation; matrix equation; general solution
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
