| 关于华罗庚行列式不等式的等式条件的注记 |
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| 引用本文： | 杨忠鹏. 关于华罗庚行列式不等式的等式条件的注记[J]. 数学的实践与认识, 2006, 36(4): 222-225 |
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| 作者姓名： | 杨忠鹏 |
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| 作者单位： | 莆田学院数学系,福建,莆田,351100 |
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| 基金项目： | 福建省自然科学基金;莆田学院校科研和教改项目 |
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| 摘 要： | 在多复变分析的研究中,华罗庚(1955年)发现并证明了行列式不等式:如果n×n复矩阵A,B满足I-AAH,I-BBH都是正定矩阵,则det(I-AAH)det(I-BBH)+det(A-B)2 det(I-ABH)2,仅当A=B时取等号.我们给出了华罗庚行列式不等式的等式成立的充分必要条件.
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| 关 键 词： | 复矩阵 行列式 不等式 等式条件 |
| 修稿时间： | 2004-03-18 |
A Note About The Equality Condition of Hua Loo-Keng Inequalities of Determinants |
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| YANG Zhong-peng. A Note About The Equality Condition of Hua Loo-Keng Inequalities of Determinants[J]. Mathematics in Practice and Theory, 2006, 36(4): 222-225 |
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| Authors: | YANG Zhong-peng |
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| Abstract: | In the study of the of functions of several complex variables,Hua Loo-Keng discovered and proved the following determinant inequality: If A,B are n×n complex matrices and I-AA~H and I-BB~H are Hermitian positive definite matrices,then det(I-AA~H)det(I-BB~H)+｜det(A-B)｜~2｜det(I-AB~H)｜~2,with equality only if A=B.In this paper,necessary and sufficient conditions that the equality holds for Hua Loo-Keng inequality of determinant are presented. |
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| Keywords: | complex matrices determinant inequality equality condition |
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