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.
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.
作者
张华民
殷红彩
ZHANG Huamin YIN Hongcai(Department of Mathematics ~ Physics, Bengbu University, Benghu 233030,Anhui Province, China School of Management Science and Engineering, Anhui University of Finance ＆ Economics, Bengbu 233000, Anhui Province, China)
出处
《浙江大学学报（理学版）》
CAS
CSCD
北大核心
2017年第5期511-515,共5页
Journal of Zhejiang University（Science Edition）
基金
Supported by Natural Science Foundation of Anhui Provincial Education Department(KJ2016A458)
Excellent Personnel Domestic Visiting Project(gxfxZD2016274)
关键词
正定矩阵
特征值
特征向量
行列式不等式
positive definite matrix
eigenvalue
eigenvector
determinant inequality
