Solving quaternion generalized Sylvester matrix equations based on semi-tensor product of matrices
SUN Jianhua， LI Ying， ZHANG Mingcui， XI Yimeng
(Research Center of Semi-tensor Product of Matrices： Theory and Applications， College of Mathematical Sciences， Liaocheng University， Liaocheng 252000， Shandong， China)
Abstract：In this paper， the quaternion generalized Sylvester matrix equations are solved by using semi-tensor product of matrices. Firstly， semi-tensor product of real matrices is generalized to quaternion matrices， and then some new conclusions of quaternion matrix under vector operator are proposed by using semi-tensor product of quaternion matrices. Using these conclusions， quaternion matrix equations are transformed into quaternion linear equations， and finally into real linear equations. Consequently， the necessary and sufficient conditions for the compatibility and the expression of general solutions of equations are obtained， and the minimal norm solutions are given. Finally， numerical examples show the effectiveness of the method.
2024, Vol. 58 
