| 一些数值不等式的矩阵形式推广 |
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| 引用本文： | 刘静,耿宏瑞. 一些数值不等式的矩阵形式推广[J]. 西南师范大学学报(自然科学版), 2012, 37(6): 5-8 |
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| 作者姓名： | 刘静 耿宏瑞 |
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| 作者单位： | 重庆大学数学与统计学院,重庆,401331 |
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| 摘 要： | 利用2个正定Hermite矩阵在交换条件下可同时对角化的性质,给出了平方、算术、几何、调和平均不等式的矩阵形式,并在此基础上对Hlder不等式和Minkowski不等式作出了进一步推广.
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| 关 键 词： | 正定Hermite矩阵 Hlder不等式 Minkowski不等式 |
The Promotion of Some Numerical Matrix Inequalities |
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| LIU Jing , GENG Hong-rui. The Promotion of Some Numerical Matrix Inequalities[J]. Journal of southwest china normal university(natural science edition), 2012, 37(6): 5-8 |
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| Authors: | LIU Jing GENG Hong-rui |
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| Affiliation: | School of Mathematics and Statistics,Chongqing University,Chongqing 401331,China |
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| Abstract: | By applying the properties that pairs of commutate matrices can be simultaneously diagonalized,the matrix version of the square,arithmetic,geometric,harmonic mean inequalities are given.Some further generalizations of the Hlder and Minkowski inequalities are obtained based on the results above. |
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| Keywords: | positive definite Hermite matrix Hlder inequality Minkowski inequality |
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