| 任意除环上的矩阵方程AX+YA=C |
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| 引用本文： | 钮宏霞. 任意除环上的矩阵方程AX+YA=C[J]. 曲阜师范大学学报, 2003, 29(3): 39-40 |
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| 作者姓名： | 钮宏霞 |
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| 作者单位： | 潍坊学院数学系 261041，山东省潍坊市 |
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| 摘 要： | 设F是一个任意的除环，给出了F上的矩阵方程AX YA=C有解的充要条件及其通解的表达公式，作为特例，得到了矩阵方程AX=C和YA=C有解的充要条件及其通解表达式。
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| 关 键 词： | 除环 矩阵方程 充要条件 通解 奇异值分解定理 初等变换 |
| 文章编号： | 1001-5337(2003)03-0039-02 |
| 修稿时间： | 2002-10-07 |
THE MATRIX EQUATION AX+YA=C OVER AN ARBITARY DIVISION RING |
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| NIU Hong-xia. THE MATRIX EQUATION AX+YA=C OVER AN ARBITARY DIVISION RING[J]. Journal of Qufu Normal University(Natural Science), 2003, 29(3): 39-40 |
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| Authors: | NIU Hong-xia |
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| Abstract: | The matrix equationAX+YA=C over an arbitrary division ring is studied. A necessary and sufficient condition for the existence and the expression of the general solution of matrix equation are derived. As a particular case, the corresponding results of the matrix equationsAX=C andYA=C are obtained. |
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| Keywords: | matrix equation division ring general solution |
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