| 三次矩阵方程的解的判定 |
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| 引用本文： | 李凤伟.三次矩阵方程的解的判定[J].大学数学,2009,25(3). |
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| 作者姓名： | 李凤伟 |
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| 作者单位： | 枣庄学院,数学与信息科学系,山东,枣庄,277160 |
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| 摘 要： | 给定A∈Mn(F),g(x)=x3+ax2+bx+c∈Fx],本文讨论矩阵方程g(X)=A的解的存在性问题.在Li′s研究的基础上,当f(x)=p1(x)p2(x)…ps(x)时,我们给出g(X)=A有解的充要条件为对每一个pi(x),pi(g(x))在Fx]中存在ni次因式,ni=degpi(x).
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| 关 键 词： | 特征多项式 分裂域 最小多项式 |
The Judgement of the Solution about Three Degree Matrix Equations |
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| LI Feng-wei.The Judgement of the Solution about Three Degree Matrix Equations[J].College Mathematics,2009,25(3). |
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| Authors: | LI Feng-wei |
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| Institution: | Dept.of Math.and Information Science;Zaozhuang University;Zaozhuang 277160;China |
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| Abstract: | Given A∈Mn(F),g(x)=x3+ax2+bx+c∈Fx],in this paper,we consider the existence of solution about matrix equations g(X)=A.Based on Li′s study,when f(x)=p1(x)p2(x)…ps(x),we show that matrix equations g(X)=A have a solution B∈Mn(F) if and only if for every pi(x),pi(g(x)) has a factor of degree ni,where ni=degpi(x). |
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| Keywords: | characteristic polynomial splitting field minimal polynomial |
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