| 除环上左线性方程组的反问题 |
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| 引用本文： | 王卿文,林春艳.除环上左线性方程组的反问题[J].数学研究,1996,29(2):91-95. |
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| 作者姓名： | 王卿文 林春艳 |
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| 作者单位： | 山东昌潍师院数学系，山东财政学院基础部 |
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| 摘 要： | 推广并改进了实数域上线性方程组的反问题及其一系列结果，解决了除环上左线性方程组更具广泛性的一类反问题，给出了此类反问题有（斜）自共轭解及（半）正定自共轭解的充要条件及其解集结构．
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| 关 键 词： | 除环，线性方程组反问题，（斜）自共轭矩阵，（半）正定矩阵 |
An Inverse Problem of a System of Linear Left Equations over Skew Fields |
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| Wang Qingwen.An Inverse Problem of a System of Linear Left Equations over Skew Fields[J].Journal of Mathematical Study,1996,29(2):91-95. |
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| Authors: | Wang Qingwen |
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| Abstract: | In this paper,we generalize and improve the inverse problem of a system of linear equations over real field. We solve the more general inverse problem of a system of linear left equations over skew fields. Necessary and sufficient conditions for the existence of and the expressions for (skew) self-conjugate solutions and positive(semi)definite self-conjugate solutions of the present inverse problem are obtawined. |
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| Keywords: | division ring inverse problem of a system of linear equations (skew)self-conjugate matrix positive (semi)definite self-conjugate matrix |
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