REFINEMENTS OF THE HADAMARD AND CAUCHY-SCHWARZ INEQUALITIES WITH TWO INEQUALITIES OF THE PRINCIPAL ANGLES

被引：16

作者：

Zhang, Huamin ^{[1
]}

Yin, Hongcai ^{[2
]}

机构：

[1] Anhui Sci & Technol Univ, Coll Informat & Network Engn, Bengbu 233030, Peoples R China

[2] Anhui Univ Finance & Econ, Sch Management Sci & Engn, Bengbu 233000, Peoples R China

来源：

JOURNAL OF MATHEMATICAL INEQUALITIES | 2019年 / 13卷 / 02期

关键词：

Parallelotope volume formula; Hadamard inequality; Cauchy-Schwarz inequality; principal angle inequality; MATRIX; PARALLELOTOPES; ALGORITHMS; STABILITY; PRODUCT; JACOBI;

D O I：

10.7153/jmi-2019-13-28

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By discussing two volume formulae for the parallelotope, some refinements of the Hadamard and Cauchy-Schwarz inequalities are given and a class of principal inequalities related a parallelotope is established. This class of principal inequalities have a close relation to the Hadamard and Fischer determinant inequalities. By using the interlacing property, a principal inequality related to two subspaces is given which has a close relation to the Koteljanskii determinant inequality. Analysis indicates that these two principal inequalities can be extended to two class of principal inequalities easily.

引用

页码：423 / 435

页数：13

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