| On a Solution of the Quaternion Matrix Equation X - A X B = C and Its Application |
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| 引用本文： | Tong Song JIANG Mu Sheng WEI. On a Solution of the Quaternion Matrix Equation X - A X B = C and Its Application[J]. 数学学报(英文版), 2005, 21(3): 483-490. DOI: 10.1007/s10114-004-0428-x |
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| 作者姓名： | Tong Song JIANG Mu Sheng WEI |
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| 作者单位： | [1]Department of Mathematics, Linyi Teacher＇s University, Linyi 276005, P. R. China [2]Department of Computer Science and Technology, Shandong University, Jinan 250100, P. R. China [3]Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China |
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| 基金项目： | Supported by the National Natural Science Foundation of China （10371044） and Shanghai Priority AcademicDiscipline Foundation, Shanghai, China |
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| 摘 要： | ![]()
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| 关 键 词： | 四元数矩阵方程 存在性 复合矩阵 表示法 |
| 收稿时间： | 2002-05-17 |
| 修稿时间： | 2002-05-172003-04-17 |
On a Solution of the Quaternion Matrix Equation X - Atilde{X}B = Cand Its Application |
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| Tong Song Jiang,Mu Sheng Wei. On a Solution of the Quaternion Matrix Equation X - Atilde{X}B = Cand Its Application[J]. Acta Mathematica Sinica(English Series), 2005, 21(3): 483-490. DOI: 10.1007/s10114-004-0428-x |
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| Authors: | Tong Song Jiang Mu Sheng Wei |
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| Affiliation: | (1) Department of Mathematics, Linyi Teacher’s University, Shandong 276005, P. R. China;(2) Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China;(3) Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China |
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| Abstract: | ![]()
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. |
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| Keywords: | Quaternion matrix equation Solution Real representation |
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