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| 一类矩阵特征值的不等式及其在Fischer不等式证明中的应用 | |
| 引用本文： | 张华民,殷红彩.一类矩阵特征值的不等式及其在Fischer不等式证明中的应用[J].浙江大学学报(理学版),2017,44(5):511-515. |
| 作者姓名： | 张华民 殷红彩 |
| 作者单位： | 1. 蚌埠学院 数理系, 安徽 蚌埠 233030; 2. 安徽财经大学 管理科学和工程学院, 安徽 蚌埠 233000 |
| 基金项目： | Supported by Natural Science Foundation of Anhui Provincial Education Department (KJ2016A458) and Excellent Personnel Domestic Visiting Project (gxfxZD2016274). |
| 摘 要： | Hadamard和Fischer不等式在矩阵研究中起重要作用.已有大量文献研究此两不等式的新证明、推广、细化及应用.本文研究了和实对称正定矩阵相关的一类矩阵的特征值，并建立了关于这类矩阵特征值乘积范围的一个不等式，利用此不等式证明了行列式的Fischer和Hadamard不等式. |
| 关 键 词： | 正定矩阵 特征值 特征向量 行列式不等式 |
| 收稿时间： | 2016-02-04 |
An eigenvalue inequality of a class of matrices and its applications in proving the Fischer inequality |
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| ZHANG Huamin,YIN Hongcai.An eigenvalue inequality of a class of matrices and its applications in proving the Fischer inequality[J].Journal of Zhejiang University(Sciences Edition),2017,44(5):511-515. | |
| Authors: | ZHANG Huamin YIN Hongcai |
| Institution: | 1. Department of Mathematics & Physics, Bengbu University, Bengbu 233030, Anhui Province, China; 2. School of Management Science and Engineering, Anhui University of Finance & Economics, Bengbu 233000, Anhui Province, China |
| Abstract: | The Hadamard inequality and Fischer inequality play an important role in the matrix study. Many articles have addressed these inequalities providing new proofs, noteworthy extensions, generalizations, refinements, counterparts and applications. This paper discusses the eigenvalues of a class of matrices related to the real symmetric positive definite matrix and establishes an inequality of the eigenvalues. By using this inequality, the Fischer determinant inequality and Hadamard determinant inequality are proved. |
| Keywords: | positive definite matrix eigenvalue eigenvector determinant inequality |
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