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.
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页码：423 / 435
页数：13
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