REFINEMENTS OF TWO DETERMINANTAL INEQUALITIES FOR POSITIVE SEMIDEFINITE MATRICES

被引：4

作者：

Hong, Yan ^{[1
]}

Qi, Feng ^{[2
,3
]}

机构：

[1] Inner Mongolia Minzu Univ, Coll Math & Phys, Tongliao 028043, Inner Mongolia, Peoples R China

[2] Henan Polytech Univ, Inst Math, Jiaozuo 454003, Henan, Peoples R China

[3] Tiangong Univ, Sch Math Sci, Tianjin 300387, Peoples R China

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2022年 / 25卷 / 03期

关键词：

Determinantal inequality; eigenvalue; positive semidefinite matrix; determinant;

D O I：

10.7153/mia-2022-25-42

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A,B,C is an element of C-n Chi n be positive semidefinite matrices and let |A|, |B|, |C| be determinants of A, B,C is an element of C-n Chi n respectively. In this paper, the authors prove two determinantal inequalities |A+ B+C| + |C| >= |A+ C| + |B+ C| + (2(n) - 2) |AB|(1/ 2) + 3(3(n-1) - 2(n) + 1) |ABC|(1/3) and |A+ B+ C| + |A| + |B| + |C| >= |A+ B| + |A+ C| + |B+ C| + 3(3(n-1) - 2(n) + 1) |ABC|(1/3). These two inequalities refine known ones.

引用

页数：1