| Bapat-Kwong矩阵不等式的推广 |
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| 引用本文： | 杨忠鹏.Bapat-Kwong矩阵不等式的推广[J].数学杂志,2007,27(1):88-92. |
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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;福建省教育厅科研项目;莆田学院校科研和教改项目 |
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| 摘 要： | 本文研究了两个经典的Hermitian正定矩阵的Hadamard乘积的Bapat-Kwong矩阵不等式的推广,利用局部完全Hermitian矩阵的性质,根据可逆矩阵的主子矩阵与其Schur补的关系,得到了两个局部完全Hermitian矩阵的Hadamard乘积的矩阵不等式.所得到的结果不仅在放弃了正定性的前提下得到了经典的Bapat-Kwong矩阵不等式,而且还给出了这个矩阵不等式等式成立的充分必要条件.
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| 关 键 词： | Hadamard乘积 局部完全Hermitian矩阵 矩阵不等式 等式条件 |
| 文章编号： | 0255-7797（2007）01-0088-05 |
| 修稿时间： | 2004-10-142005-04-08 |
A GENERALIZATION OF BAPAT-KWONG MATRIX INEQUALITY |
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| YANG Zhong-peng.A GENERALIZATION OF BAPAT-KWONG MATRIX INEQUALITY[J].Journal of Mathematics,2007,27(1):88-92. |
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| Authors: | YANG Zhong-peng |
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| Institution: | Dept. of Math., Putian University, Putian 351100, China |
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| Abstract: | In this paper, we study the generalization of the classic Bapat-Kwong matrix inequality for the Hadamard product of two Hermitian positive definite matrices. Then making use of the properties of local complete Hermitian matrix and the relation between principal submatrices of the invertible matrix and its Schur complements, we obtain a matrix inequality for the Hadamard product of two local complete Hermitian matrices. From the result, we not only obtain the classic Bapat-Kwong matrix inequality without positive definite properties, but also present a necessary and sufficiency condition such that the equality in that matrix inequality holds. |
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| Keywords: | Hadamard product local complete Hermitian matrix matrix inequality condition of equality |
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