| QUATERNION GENERALIZED SINGULAR VALUE DECOMPOSITION AND ITS APPLICATIONS |
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| 作者姓名： | Jiang Tongsong Liu Yonghui Wei Musheng |
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| 作者单位： | [1]Dept. of Math. , Linyi Normal Univ. , Shandong 276005,China [2]Dept. of Comput. Sci. and Tech. , Shandong Univ. , Jinan 250100, China. [3]Dept. of Math. , East China Normal Univ. , Shanghai 200062,China |
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| 基金项目： | Supported by the National Natural Science Foundation of China （10371044） and Natural Science Foundation of Shandong. |
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| 摘 要： | This paper derives a theorem of generalized singular value decomposition of quaternion matrices （QGSVD）,studies the solution of general quaternion matrix equation AXB -CYD= E,and obtains quaternionic Roth＇s theorem. This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.
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| 关 键 词： | QGSVD 四元矩阵方程 Roth理论 奇异值 存在性 |
| 收稿时间： | 2004-12-21 |
Quaternion generalized singular value decomposition and its applications |
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| Jiang Tongsong Liu Yonghui Wei Musheng.QUATERNION GENERALIZED SINGULAR VALUE DECOMPOSITION AND ITS APPLICATIONS[J].Applied Mathematics A Journal of Chinese Universities,2006,21(1):113-118. |
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| Authors: | Jiang Tongsong Liu Yonghui Wei Musheng |
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| Institution: | (1) Dept. of Math., Linyi Normal Univ., 276005 Shandong, China;(2) Dept. of Comput. Sci. and Tech., Shandong Univ., 250100 Jinan, China;(3) Dept. of Math., East China Normal Univ., 200062 Shanghai, China |
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| Abstract: | . This paper derives a theorem of generalized singular value decomposition of quaternion matrices(QGSVD),studies the solution of general quaternion matrix equation AXB-CYD=E,and obtains quaternionic Roth's theorem.This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation. |
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| Keywords: | QGSVD quaternion matrix equation Roth's theorem |
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