| Cauchy-Buniakowski不等式的矩阵形式 |
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| 引用本文： | 汪华,李爱华.Cauchy-Buniakowski不等式的矩阵形式[J].长江大学学报(社会科学版),2001(2). |
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| 作者姓名： | 汪华 李爱华 |
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| 作者单位： | 荆州师范学院数学系11981班!434104 |
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| 摘 要： | Cauchy -Buniakowski不等式是Euclid空间理论的重要基石之一 ,文献 1,2 ]都给出了该不等式的向量内积形式 .本文考虑矩阵乘积形式的Cauchy -Buniakowski不等式 ,通过在矩阵间引入偏序关系 ,讨论对称矩阵及Hermite矩阵的某些性质 ,得到矩阵形式的Cauchy -Buniakowski不等式和三角形不等式 ,从而推广了文献 1,2 ]的结果
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| 关 键 词： | Cauchy-Buniakowski不等式 三角形不等式 偏序 半正定矩阵 Hermite矩阵 |
CAUCHY-BUNIAKOWSKI INEQUALITY IN THE FORM OF MATRICES |
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| Wang Hua,Li Aihua.CAUCHY-BUNIAKOWSKI INEQUALITY IN THE FORM OF MATRICES[J].Journal of Yangtze University:Social Sciences,2001(2). |
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| Authors: | Wang Hua Li Aihua |
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| Abstract: | Cauchy-Buniakowski inequality is one of the important bases of the theories of Euclid (or unitary)spaces. In this paper, by introducing a bias order relation,the author discussed symmetrical (or Hermitian) matrices, got the matrix type Cauchy-Buniakowski inequality and therefore extended the results in reference 1,2]. |
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| Keywords: | Cauchy-Buniakowski inequality triangle inequality bias order positive semi-definite matrix Hermite matrix |
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