Norm inequalities for matrix geometric means of positive definite matrices

被引：7

作者：

Fujii, Jun Ichi ^{[1
]}

Seo, Yuki ^{[2
]}

Yamazaki, Takeaki ^{[3
]}

机构：

[1] Osaka Kyoiku Univ, Dept Art & Sci Informat Sci, Osaka 543, Japan

[2] Osaka Kyoiku Univ, Dept Math Educ, Osaka 543, Japan

[3] Toyo Univ, Dept Elect Elect & Comp Engn, Saitama, Japan

来源：

LINEAR & MULTILINEAR ALGEBRA | 2016年 / 64卷 / 03期

关键词：

Karcher mean; chaotic geometric mean; matrix geometric mean; unitarily invariant norm; Kantorovich constant; Ando-Hiai inequality;

D O I：

10.1080/03081087.2015.1051939

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain eigenvalue inequalities for matrix geometric means of positive definite matrices. This implies matrix norm inequalities for unitarily invariant norms, which are considered as complementary to a series of norm inequalities among geometric means. We give complements of the Ando-Hiai type inequality for the Karcher mean by means of the generalized Kantorovich constant. Finally, we consider the monotonicity of the eigenvalue function for the Karcher mean.

引用

页码：512 / 526

页数：15

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