Singular Value Inequalities of Matrix Sum in Log-majorizations

被引：1

作者：

Xi, Bo Yan ^{[1
]}

Zhang, Fu Zhen ^{[2
]}

机构：

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

[2] Nova Southeastern Univ, Dept Math, 3301 Coll Ave, Ft Lauderdale, FL 33314 USA

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2023年 / 39卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Eigenvalue; Hoffman minimax theorem; Hua determinant inequality; log-majorization; majorization; Minkowski determinant inequality; singular value; Wielandt minimax theorem; EIGENVALUES; PRODUCT;

D O I：

10.1007/s10114-023-1512-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show some upper bounds for the product of arbitrarily selected singular values of the sum of two matrices. The results are additional to our previous work on the lower bound eigenvalue inequalities of the sum of two positive semidefinite matrices. Besides, we state explicitly Hoffman's minimax theorem with a proof, and as applications of our main results, we revisit and give estimates for related determinant inequalities of Hua type.

引用

页码：375 / 386

页数：12

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