DETERMINANTAL INEQUALITIES OF POSITIVE DEFINITE MATRICES

被引：7

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.

引用

页码：167 / 172

页数：6