| 关于四元数矩阵方程AX+YA=C的三种解 |
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| 引用本文： | 黄敬频. 关于四元数矩阵方程AX+YA=C的三种解[J]. 哈尔滨师范大学自然科学学报, 2004, 20(1): 31-34 |
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| 作者姓名： | 黄敬频 |
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| 作者单位： | 广西民族学院 |
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| 基金项目： | 广西民族学院科研基金资助项目 (0 2SJX0 0 0 8) |
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| 摘 要： | 本文利用四元数矩阵的奇异值分解给出了四元数矩阵方程AX YA=C分别存在一般解、自共轭解、正定自共轭解的充要条件及其通解的表达式．
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| 关 键 词： | 四元数体 矩阵方程 奇异值分解 自共轭矩阵 正定自共轭矩阵 |
| 修稿时间： | 2003-12-05 |
THREE CATEGORIES SOLUTION ON THE QUATERNION MATRIXC EQUATION AX + YA = C |
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| Huang Jingpin. THREE CATEGORIES SOLUTION ON THE QUATERNION MATRIXC EQUATION AX + YA = C[J]. Natural Science Journal of Harbin Normal University, 2004, 20(1): 31-34 |
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| Authors: | Huang Jingpin |
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| Affiliation: | Guangxi University for Nationalities |
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| Abstract: | Using the singular value decomposition of quaternion matrices, this paper gives necessary and sufficient conditions for quaternion matrix equation AX+YA=C to have the general solution, the self-conjugate solution and the positive definite self-conjugate solution, and their general form of the solutions has been provided. |
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| Keywords: | Quaternion field Matrix equation Singular value decomposition Self-conjugate matrix Positive difinite self-conjugate matrix |
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