| 关于正定矩阵的一类不等式 |
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| 引用本文： | 游光荣. 关于正定矩阵的一类不等式[J]. 国防科技大学学报, 1988, 10(1): 70-75 |
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| 作者姓名： | 游光荣 |
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| 作者单位： | 国防科技大学系统工程与应用数学系 硕士生 |
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| 摘 要： | 本文考虑了常见的Hlder不等式和算术——几何平均不等式在矩阵中的类似,对R.Bellman提出的两个问题[1]给出了肯定的回答。同时建立了Cauchy-schwarz不等式及其增补在矩阵中的类似。
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| 关 键 词： | 不等式 矩阵 迹 特征值 |
| 收稿时间： | 1987-06-01 |
A Class of Inequalities for Positive Definite Matrices |
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| You Guangrong. A Class of Inequalities for Positive Definite Matrices[J]. Journal of National University of Defense Technology, 1988, 10(1): 70-75 |
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| Authors: | You Guangrong |
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| Affiliation: | You Guangrong |
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| Abstract: | In this paper, we first consider a matrix analogue of H(?)lder's inequality.Furthermore, we obtain a matrix analogue of the arithmetric-geometric-meaninequality. Then we give an affirmative answer to two open questions ofR. Bellman. After that, we obtain a matrix analogue of Cauchy-Schwarzinequality and its complementary (or reverse) inequalities. We derive asimilar result for nonnegative matrices. |
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| Keywords: | Inequality Matrix Trace Eigenvalue |
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