An eigenvalue inequality of a class of matrices and its applications in proving the Fischer inequality
ZHANG Huamin1, YIN Hongcai2
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.
基金资助:Supported by Natural Science Foundation of Anhui Provincial Education Department (KJ2016A458) and Excellent Personnel Domestic Visiting Project (gxfxZD2016274).
作者简介: 张华民(1972-),ORCID:http://orcid.org/0000-0002-7416-7415,male,doctor,associate professor,the field of interest are matrix theory and its applications,E-mail:zhangeasymail@126.com.
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.
ZHANG Huamin, YIN Hongcai. An eigenvalue inequality of a class of matrices and its applications in proving the Fischer inequality. Journal of ZheJIang University(Science Edition), 2017, 44(5): 511-515.
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