Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices

被引：14

作者：

Li, Yao-Tang ^{[1
,2
]}

Li, Yan-Yan ^{[1
]}

Wang, Rui-Wu ^{[2
]}

Wang, Ya-Qiang ^{[1
]}

机构：

[1] Yunnan Univ, Sch Math & Stat, Kunming 650091, Yunnan, Peoples R China

[2] Chinese Acad Sci, Kunming Inst Zool, State Key Lab Genet Resources & Evolut, Kunming 650223, Yunnan, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2010年 / 432卷 / 2-3期

基金：

中国国家自然科学基金;

关键词：

Nonnegative matrix; M-matrix; Hadamard product; Fan product; Spectral radius; Minimum eigenvalue; CONJECTURE; FIEDLER; MARKHAM; INVERSE;

D O I：

10.1016/j.laa.2009.08.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A and B be nonsingular M-matrices. A lower bound on the minimum eigenvalue q(B circle A(-1)) for the Hadamard product of A(-1) and B, and a lower bound on the minimum eigenvalue q(A star B) for the Fan product of A and B are given. In addition, an upper bound on the spectral radius rho(A circle B) of nonnegative matrices A and B is also obtained. These bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depending on the entries of matrices A and B. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：536 / 545

页数：10

共 10 条

[1]

[Anonymous], 1979, NONNEGATIVE MATRICES

[2]

Chen X. H., 2000, SPECIAL MATRIX

[3] Bounds on eigenvalues of the Hadamard product and the Fan product of matrices [J].

Fang, Maozhong .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 425 (01) :7-15

[4]

FIEDLER M, 1988, LINEAR ALGEBRA APPL, V101, P1

[5]

Horn RA., 2013, MATRIX ANAL

[6] Some inequalities for the Hadamard product and the Fan product of matrices [J].

Huang, Rong .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 428 (07) :1551-1559

[7] New lower bounds on eigenvalue of the Hadamard product of an M-matrix and its inverse [J].

Li, Yao-Tang ;

Chen, Fu-Bin ;

Wang, De-Feng .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (04) :1423-1431

[8] MINIMAL GERSCHGORIN SETS [J].

VARGA, RS .

PACIFIC JOURNAL OF MATHEMATICS, 1965, 15 (02) :719-&

[9] On a conjecture of Fiedler and Markham [J].

Yong, XR ;

Wang, Z .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 288 (1-3) :259-267

[10] Proof of a conjecture of Fiedler and Markham [J].

Yong, XR .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 320 (1-3) :167-171

← 1 →