Application of semi-tensor product of matrices in solving quaternion linear system
WEI Anli， LI Ying， ZHAO Jianli， DING Wenxu
(School of Mathematical Sciences Research Center of Semi-tensor Product of Matrices： Theory and Applications，Liaocheng University， Liaocheng 252000， Shandong， China)
Abstract：In recent years， the semi-tensor product of matrices is widely applied to the analysis and control of Boolean network， mix-valued logical network， power system nonlinear robust stability control algebra problem and so on. In this paper， a new kind of applications in quaternion linear system is proposed. By using semi-tensor product， a real vector representation of quaternion， and the special structure of quaternion tridiagonal Hermitian (Anti-Hermitian) matrix， the expression of the least squares tridiagonal Hermitian (Anti-Hermitian) solution of (AXB，CXD)＝(E，F) is obtained. As the special case， the equivalent condition for the compatibility of the quaternion matrix equation and the expression of general solutions under the compatibility conditions are given. In addition， the numerical algorithm and experiment are given to verify the effectiveness of this application.
2022, Vol. 56 
