A proof of a conjectured determinantal inequality

被引：3
|
作者：
Ghabries, Mohammad M. [1 ,2 ]
Abbas, Hassane [3 ]
Mourad, Bassam [3 ]
Assi, Abdallah [1 ]
机构：
[1] LAREMA, Fac Sci, Dept Math, Angers, France
[2] Lebanese Univ, Fac Sci, Dept Math, KALMA, Beirut, Lebanon
[3] Lebanese Univ, Fac Sci, Dept Math, Beirut, Lebanon
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2020年 / 605卷
关键词：
Determinantal inequalities; Hermitian matrix; Positive semi-definite matrix; Log-majorization; Eigenvalues;
D O I：
10.1016/j.laa.2020.07.013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The main goal of this paper is to prove the following determinantal inequality: det(A(k) + vertical bar B-s/2 A(s/2)vertical bar(2t/s)) <= (A(k) + A(t) B-t) <= det (A(k) + + vertical bar A(s/2) B-s/2 vertical bar(2t/s)) for any positive semi-definite matrices A and B, and for all 0 <= t <= s <= k. It generalizes several known determinantal inequalities, and one main consequence of it confirms Lin's conjecture which states that for positive semi-definite matrices A and B, det(A(2) + A(t) B-t) <= det(A(2) + vertical bar AB vertical bar(t)) for 0 <= t <= 2. We conclude with another related determinantal inequality. (C) 2020 Elsevier Inc. All rights reserved.
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页码：21 / 28
页数：8
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