| 关于正定厄米特矩阵的Schur补的迹和特征值的不等式 |
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| 引用本文： | 黄弘.关于正定厄米特矩阵的Schur补的迹和特征值的不等式[J].数学杂志,2007,27(2):188-190. |
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| 作者姓名： | 黄弘 |
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| 作者单位： | 武汉大学数学与统计学院,湖北武汉,430072 |
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| 基金项目： | 国家重点基础研究发展计划(973计划) |
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| 摘 要： | 本文研究了正定厄米特矩阵Schur补的迹和特征值的性质,通过一个不等式的证明,得到了正定厄米特矩阵和的Schur补与正定厄米特矩阵Schur补的和的迹和特征值之间的不等式.
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| 关 键 词： | 矩阵的迹 不等式 Schur补 半正定厄米特矩阵 |
| 文章编号： | 0255-7797（2007）-02-0188-03 |
| 修稿时间： | 2005-01-172005-04-08 |
THE INEQUALITY ON TRACE AND EIGENVALUES OF THE SCHUR COMPLEMENT OF A POSITIVE SEMIDEFINITE HERMITIAN MATRIX |
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| HUANG Hong.THE INEQUALITY ON TRACE AND EIGENVALUES OF THE SCHUR COMPLEMENT OF A POSITIVE SEMIDEFINITE HERMITIAN MATRIX[J].Journal of Mathematics,2007,27(2):188-190. |
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| Authors: | HUANG Hong |
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| Institution: | School of Math. and Statistics, Wuhan University, Wuhan 430072, China |
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| Abstract: | In this paper, we study the trace and the eigenvalues of a positive definite Hermitian matrix and get inequalities about the trace and eigenvalues between the Schur complement of the sum of positive definite Hermiteian matrix and the sum of the Schur complements of positive definite Hermiteian matrix by proving an inequality. |
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| Keywords: | trace of a matrix inequality Schur complement positive semidefinite Hermitian matrix |
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