SOME EIGENVALUE INEQUALITIES FOR POSITIVE SEMIDEFINITE MATRIX POWER PRODUCTS

被引：22

作者：

WANG, BY

GONG, MP

机构：

[1] Department of Mathematics Beijing Normal University Beijing

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1993年 / 184卷

关键词：

D O I：

10.1016/0024-3795(93)90382-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the eigenvalues of positive semidefinite matrix power products and obtain some inequalities, most of which are in terms of majorization. In particular, for A, B greater-than-or-equal-to 0, beta > alpha > 0, we prove log lambda1/alpha(A(alpha)B(alpha)) curly less than log lambda1/beta(A(beta)B(beta)). The result is a generalization of some work of Marcus, Lieb, Thirring, Le Couteur, Bushell, and Trustrum.

引用

页码：249 / 260

页数：12

共 6 条

[1] MAJORIZATION, DOUBLY STOCHASTIC MATRICES, AND COMPARISON OF EIGENVALUES
ANDO, T
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1989, 118 : 163 - 248
[2] TRACE INEQUALITIES FOR POSITIVE DEFINITE MATRIX POWER PRODUCTS
BUSHELL, PJ
TRUSTRUM, GB
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1990, 132 : 173 - 178
[3] LECOUTEUR KJ, 1980, J PHYS A-MATH GEN, V13, P3147, DOI 10.1088/0305-4470/13/10/012
[4] Lieb EH., 1976, STUDIES MATH PHYS, P269
[5] Marcus M., 1956, AM MATH MONTHLY, V63, P173
[6] Marshall A. W., 1979, INEQUALITIES MAJORIZ

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