| 矩阵行标准形定理的一个证明 |
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| 引用本文： | 何延治.矩阵行标准形定理的一个证明[J].延边大学理工学报,2011(4):327-329. |
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| 作者姓名： | 何延治 |
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| 作者单位： | 延边大学理学院数学系,吉林延吉133002 |
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| 基金项目： | 延边大学教育教学研究课题（延大教发[2010]第8号） |
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| 摘 要： | 利用矩阵的行初等变换与向量方程，运用反证法给出了矩阵行标准形定理的1个新的证明方法．本文结果为线性方程组的系统理论的教学可在行列式、逆矩阵、向量线性相关与秩的理论之前进行奠定了理论基础，可作为文献1一tO]在处理矩阵行标准形定理时的1个补充．
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| 关 键 词： | 简化阶梯形矩阵 行初等变换 向量方程 行标准形 |
A Proof of Row Canonical Form Theorem of Matrixes |
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| HE Yan-zhi.A Proof of Row Canonical Form Theorem of Matrixes[J].Journal of Yanbian University (Natural Science),2011(4):327-329. |
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| Authors: | HE Yan-zhi |
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| Affiliation: | HE Yan-zhi ( Department of Mathematics, College of Science, Yanbian University, Yanji 133002, China ) |
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| Abstract: | Using matrix row elementary transformation and vector equations, we gave a new proof method of a row canonical form theorem of matrixes by reduction to absurdity. It laid a theoretical foundation for teaching the theory of linear equations systems before the theories of determinant, inverse matrix, linear dependence of vector and rank. The results show that it can be used as a supplement to handl the theorem in references 1-10]. |
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| Keywords: | reduced step matrix row elementary transformation vector equations row canonical formof matrix |
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