Dual Quaternion Matrix Equation AXB = C with Applications.

Autor:	Chen, Yan, Wang, Qing-Wen, Xie, Lv-Ming
Předmět:	QUATERNIONS AUTOMATIC differentiation EQUATIONS COMPUTER graphics HERMITIAN forms MATRICES (Mathematics) QUATERNION functions
Zdroj:	Symmetry (20738994); Mar2024, Vol. 16 Issue 3, p287, 14p
Abstrakt:	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. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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