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- Title
Dual Quaternion Matrix Equation AXB = C with Applications.
- Authors
Chen, Yan; Wang, Qing-Wen; Xie, Lv-Ming
- Abstract
Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics, and others. Due to its application in control theory, matrix equation A X B = C has been extensively studied. However, there is currently limited information on matrix equation A X B = C regarding the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of dual quaternion matrix equation A X B = C , and present the expression for the general solution when it is solvable. As an application, we derive the ϕ -Hermitian solutions for dual quaternion matrix equation A X A ϕ = 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.
- Subjects
QUATERNIONS; AUTOMATIC differentiation; EQUATIONS; COMPUTER graphics; HERMITIAN forms; MATRICES (Mathematics); QUATERNION functions
- Publication
Symmetry (20738994), 2024, Vol 16, Issue 3, p287
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym16030287