| 环上矩阵方程AXB＋CYD=E的可解性 |
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| 引用本文： | 黄礼平.环上矩阵方程AXB＋CYD=E的可解性[J].数学进展,1997,26(3):269-275. |
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| 作者姓名： | 黄礼平 |
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| 作者单位： | 湘潭矿业学院数理研究所 |
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| 基金项目： | 国家自然科学基金,湖南省自然科学基金 |
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| 摘 要： | 设Ｒ为一个含幺环，应用矩阵的｛１，２｝－逆（存在的前提下），本文得到Ｒ上矩阵方程ＡＸＢ＋ＣＹＤ＝Ｅ有解的充要条件以及一般解的公式，并且推广了著名的Ｒｏｔｈ等价定理。
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| 关 键 词： | 环 单位正则环 初等因子环 矩阵方程 可解性 |
The Solvability of Matrix Equation AXB CYD=E Over a Ring |
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| Huang Liping.The Solvability of Matrix Equation AXB CYD=E Over a Ring[J].Advances in Mathematics,1997,26(3):269-275. |
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| Authors: | Huang Liping |
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| Abstract: | Let R be a ring with identity, by using the {1, 2} inverses of matrices (if there exist), this paper obtains the necessary and sufficient conditions for existence of asolution and the explicit formulas of the general solution to the matrix equation AXB CYD=E over R , and extends the well know Roth's equivalence theorem |
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| Keywords: | ring unit regular ring elementary divisorring {1 2} inverse of a matrix matrix equation Roth's equivalence property |
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