| 线性空间相关定理及维数公式的推广和应用（英文） |
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| 引用本文： | 赵汝菊,任北上.线性空间相关定理及维数公式的推广和应用（英文）[J].广西师范学院学报(自然科学版),2011,28(4):111-118. |
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| 作者姓名： | 赵汝菊 任北上 |
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| 作者单位： | 广西师范学院数学科学学院,广西南宁,530023 |
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| 基金项目： | Supported by the Guangxi Science Foundation(2011GXNSFA018144);the Scientific Research Foundation of Guangxi Education Committee(200707LX233);the forth project of“eleven-five”of Guangxi teaching reformof higher education project |
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| 摘 要： | 线性空间的相关定理及其公式对于解决诸多代数问题提供了有力的工具,该文将线性空间中的维数公式推广到一般矩阵上,利用推广的维数公式及相应的定理来证明Sylvester不等式、Frobenius不等式等一些重要的关于秩的命题.
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| 关 键 词： | 秩 维数 不等式 维数公式 线性空间 |
Generalization and Application of Related Theorems and Dimensional Formula for Linear Space |
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| ZHAO Ru-ju,REN Bei-shang.Generalization and Application of Related Theorems and Dimensional Formula for Linear Space[J].Journal of Guangxi Teachers Education University:Natural Science Edition,2011,28(4):111-118. |
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| Authors: | ZHAO Ru-ju REN Bei-shang |
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| Institution: | (School of Mathematical Sciences,Guangxi Teachers Education University,Nanning 530023,P.R.China) |
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| Abstract: | The related theorem and formula of linear space have provided an extremely convenient tool regarding the solution to algebra question.If the linear space in dimensional formula is generalized to the general matrix,we can use the generalized dimensional formula and corresponding theorem to prove some important inequalities and equalities about the rank of matrix like Sylvester inequality,Frobenius inequality and so on. |
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| Keywords: | rank dimension inequality dimensional formula linear space |
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