| 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.[点击复制] |
| You Guangrong.A Class of Inequalities for Positive Definite Matrices[J].Journal of National University of Defense Technology,1988,10(1):70-75[点击复制] |
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| 关于正定矩阵的一类不等式 |
| 游光荣 |
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(系统工程与应用数学系)
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| 摘要: |
| 本文考虑了常见的H ?lder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不等式及其增补在短阵中的类似。 |
| 关键词: 不等式，矩阵，迹，特征值。 |
| DOI： |
| 投稿日期：1987-06-01 |
| 基金项目: |
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| A Class of Inequalities for Positive Definite Matrices |
| You Guangrong |
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(Department of Applied Mathematics and System Engineering)
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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-mean inequality. Then we give an affirmative answer to two open questions of R.Bellman.[1] After that，we obtain a matrix analogue of Cauchy-Schwarz inequality and its complementary (or reverse) inequalities. We derive a similar result for nonnegative matrices. |
| Keywords: 1nequality,Matrix,Trace,Eigenvalue |
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