On a Solution of the Quaternion Matrix Equation X-A B=C and Its Application

作     者：Tong Song JIANG Mu Sheng WEI 

作者机构：Department of Mathematics Linyi Teacher's University Linyi 276005 P. R. China Department of Computer Science and Technology Shandong University Jinan 250100 P. R. China Department of Mathematics East China Normal University Shanghai 200062 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2005年第21卷第3期

页      面：483-490页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China (10371044) Shanghai Priority Academic Discipline Foundation, Shanghai, China 

主　　题：Quaternion matrix equation Solution Real representation 

摘      要：This paper first studies the solution of a complex matrix equation X - AXB = C, obtains an explicit solution of the equation by means of characteristic polynomial, and then studies the quaternion matrix equation X - A X B = C, characterizes the existence of a solution to the matrix equation, and derives closed-form solutions of the matrix equation in explicit forms by means of real representations of quaternion matrices. This paper also gives an application to the complex matrix equation X - AXB =C.