| 关于正定矩阵的两个不等式 |
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| 引用本文： | 刘建忠,钱忠根.关于正定矩阵的两个不等式[J].数学的实践与认识,2010,40(16). |
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| 作者姓名： | 刘建忠 钱忠根 |
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| 基金项目： | 江苏省高校自然科学研究指导性计划项目 |
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| 摘 要： | 通过Hermite矩阵的谱分解及一个改进的Young不等式,得到了关于正定矩阵的两个不等式,所得结果是对一些经典的矩阵不等式的进一步推广.最后,作为应用,给出了著名的Holder不等式和Minkowsi不等式的一种反向形式.
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| 关 键 词： | 正定矩阵 矩阵函数 不等式 |
Two Inequalities of Positive Definite Matrix |
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| LIU Jian-zhong,QIAN Zhong-gen.Two Inequalities of Positive Definite Matrix[J].Mathematics in Practice and Theory,2010,40(16). |
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| Authors: | LIU Jian-zhong QIAN Zhong-gen |
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| Abstract: | In this paper,we present two inequalities of positive definite matrix by using the spectral decomposition of Hermite matrix and the improved Young inequality.These inequalities are the further generalization of some classical matrix inequalities.As an application of the obtained results,we give the reverse form of Holder inequality and Minkowski inequality. |
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| Keywords: | positive definite matrix matrix function inequality |
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