矩阵的Hadamard积和Fan积的特征值界的新估计

doi:10.16088/j.issn.1001-6600.2015.03.010

广西师范大学学报（自然科学版） ›› 2015, Vol. 33 ›› Issue (3): 66-70.doi: 10.16088/j.issn.1001-6600.2015.03.010

矩阵的Hadamard积和Fan积的特征值界的新估计

王峰

贵州民族大学理学院,贵州贵阳550025

收稿日期:2015-01-20 出版日期:2015-05-10 发布日期:2018-09-20
通讯作者: 王峰(1981—),男,山东临沂人,贵州民族大学副教授,博士。E-mail: wangf991@163.com
基金资助:
国家自然科学基金资助项目(11361074);国家数学天元基金资助项目(11326242)

New Bounds on Eigenvalue of the Hadamard Product and the Fan Product of Matrices

WANG Feng

College of Science,Guizhou Minzu University, Guiyang Guizhou 550025, China

Received:2015-01-20 Online:2015-05-10 Published:2018-09-20

摘要/Abstract

摘要： 本文给出非负矩阵A和B的Hadamard积的谱半径上界和M-矩阵A和B的Fan积的最小特征值下界的新估计式,这些估计式都只依赖于矩阵的元素,易于计算。数值例子表明,新估计式在一定条件下改进了现有的一些结果。

关键词: 非负矩阵, M-矩阵, Hadamard积, Fan积, 谱半径, 最小特征值

Abstract: A new upper bound on the spectral radius for the Hadamard product of two nonnegative matrices A and B and a new lower bound on the minimum eigenvalue for the Fan product of two M-matrices A and B are given. The estimating formulas of the bounds only depend on the entries of the matrices. Therefore, they are easy to calculate. Numerical examples show that the new formulas can improve some existing ones in some cases.

Key words: nonnegative matrix, M-matrix, Hadamard product, Fan product, spectral radius, minimum eigenvalue

中图分类号:

O151.21

王峰. 矩阵的Hadamard积和Fan积的特征值界的新估计[J]. 广西师范大学学报（自然科学版）, 2015, 33(3): 66-70.

WANG Feng. New Bounds on Eigenvalue of the Hadamard Product and the Fan Product of Matrices[J]. Journal of Guangxi Normal University(Natural Science Edition), 2015, 33(3): 66-70.

参考文献

[1] HUANG Rong. Some inequalities for the Hadamard product and the Fan product of matrices [J]. Linear Algebra Appl, 2008, 428(7):1551-1559.
[2] LIU Qing-bing, CHEN Guo-liang, ZHAO Lin-lin. Some new bounds on the spectral radius of matrices [J]. Linear Algebra Appl,2010, 432(4): 936-948.
[3] ZHAO Lin-lin. Two inequalities for the Hadamard product of matrices [J]. J Inequal Appl,2012, 2012(1):122.
[4] GUO Qian-ping, LI Hou-biao, SONG Ming-yan. New inequalities on eigenvalues of the Hadamard product and the Fan product of matrices [J]. J Inequal Appl,2013,2013(1):433.
[5] CHEN Fu-bin, REN Xian-hua, HAO Bing. Some new eigenvalue bounds for the Hadamard product and the Fan product of matrices[J]. J of Math (PRC), 2014, 34(5):895-903.
[6] 陈景良,陈向晖.特殊矩阵[M]. 北京:清华大学出版社,2001.
[7] HORN R A, JOHNSON C R. Topics in matrix analysis [M]. Cambridge: Cambridge University Press,1985.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

矩阵的Hadamard积和Fan积的特征值界的新估计

New Bounds on Eigenvalue of the Hadamard Product and the Fan Product of Matrices

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

Metrics

本文评价

推荐阅读 0

[1]	刘喜富. 一类反三角矩阵的群逆和Drazin逆[J]. 广西师范大学学报（自然科学版）, 2015, 33(3): 61-65.
[2]	张廷海. 秩-1坡矩阵的周长及保持算子[J]. 广西师范大学学报（自然科学版）, 2014, 32(3): 57-60.