DETERMINANTAL INEQUALITIES OF POSITIVE DEFINITE MATRICES

被引：6
|
作者：
Choi, Daeshik [1 ]
机构：
[1] So Illinois Univ, Edwardsville Dept Math & Stat, Box 1653, Edwardsville, IL 62026 USA
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2016年 / 19卷 / 01期
关键词：
Determinantal inequalities; Fischer's inequality; determinants of block matrices; positive definite matrices;
D O I：
10.7153/mia-19-12
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let A(i), i = 1, ..., m, be positive definite matrices with diagonal blocks A(i)((j)), 1 <= j <= k, where A(1)((j)), ..., A(m)((j)) are of the same size for each j. We prove the inequality det (Sigma(m)(i=1)A(i)(-1)) >= det(Sigma(m)(i=1)(A(i)((1)))(-1))center dot center dot center dot det(Sigma(m)(i=1)(A(i)((k)))(-1)) and more determinantal inequalities related to positive definite matrices.
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页码：167 / 172
页数：6
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