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The Dual Quaternion Matrix Equation AXB=C with Applications
Version 1
: Received: 5 February 2024 / Approved: 6 February 2024 / Online: 6 February 2024 (09:14:30 CET)
A peer-reviewed article of this Preprint also exists.
Chen, Y.; Wang, Q.-W.; Xie, L.-M. Dual Quaternion Matrix Equation AXB = C with Applications. Symmetry 2024, 16, 287. Chen, Y.; Wang, Q.-W.; Xie, L.-M. Dual Quaternion Matrix Equation AXB = C with Applications. Symmetry 2024, 16, 287.
Abstract
Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics and others. Due to its application in control theory, the matrix equation AXB=C has been extensively studied. However, there is currently limited information on matrix equation AXB=C over the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of the dual quaternion matrix equation AXB=C, and present the expression for the general solution when it is solvable. As an application, we derive the ϕ-Hermitian solutions for the dual quaternion matrix equation AXAϕ=C, where the ϕ-Hermitian extends the concepts of Hermiticity and η-Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper.
Keywords
Dual Quaternion; Moore-Penrose inverse; ϕ-Hermitian solution; matrix equations
Subject
Physical Sciences, Mathematical Physics
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.
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