Matrix inequalities by means of embedding

被引：0

作者：

Lei, TG ^{[1
]}

Woo, CW

Zhang, FZ

机构：

[1] Natl Nat Sci Fdn China, Dept Math & Phys Sci, Beijing 100085, Peoples R China

[2] City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

[3] Nova SE Univ, Div Math Sci & Technol, Ft Lauderdale, FL 33314 USA

[4] Shenyang Normal Univ, Shenyang, Peoples R China

来源：

ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2004年 / 11卷

关键词：

eigenvalue; majorization; matrix absolute value; matrix inequality; matrix norm; normal matrix; positive semidefinite matrix; singular value; spread; wielandt inequality;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this expository study some basic matrix inequalities obtained by embedding bilinear forms [Ax, x] and [Ax, y] into 2 x 2 matrices are investigated. Many classical inequalities are reproved or refined by the proposed unified approach. Some inequalities involving the matrix absolute value \A\ are given. A new proof of Ky Fan's singular value majorization theorem is presented.

引用

页码：66 / 77

页数：12

共 14 条

[1]

ANDO T, 2001, UNPUB NORMS CONES TE

[2]

ANDO T, 1998, UNPUB OPERATOR THEOR

[3]

Bellman R., 1968, LINEAR ALGEBRA ITS A, V1, P321

[4] Normal matrices: an update [J].

Elsner, L ;

Ikramov, KD .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1998, 285 (1-3) :291-303

[5]

Horn R.A., 1991, TOPICS MATRIX ANAL

[6]

Horn R. A., 1986, Matrix analysis

[7] An operator inequality and matrix normality [J].

Johnson, CR ;

Zhang, FZ .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1996, 240 :105-110

[8]

Marshall Albert W., 1979, INEQUALITIES THEORY, V143

[9] INEQUALITIES FOR NORMAL AND HERMITIAN MATRICES [J].

MIRSKY, L .

DUKE MATHEMATICAL JOURNAL, 1957, 24 (04) :591-599

[10]

Mirsky L., 1956, MATHEMATIKA, V3, P127, DOI [DOI 10.1112/S0025579300001790, 10.1112/S0025579300001790]

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