矩阵Hadamard积谱半径的新上界

钟琴<sup>1</sup>,牟谷芳<sup>2</sup>

doi:10.13718/j.cnki.xsxb.2018.12.001

西南师范大学学报(自然科学版)

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
	姓名不能为空！
邮箱
	邮箱不能为空！非法的邮箱地址。
手机号码
	电话不能为空！请输入有效手机号!
标题
	标题不能为空！
留言内容
	内容不能为空！
验证码
	验证码不能为空！验证码错误！

矩阵Hadamard积谱半径的新上界

钟琴1,牟谷芳2. 矩阵Hadamard积谱半径的新上界[J]. 西南师范大学学报(自然科学版), 2018, 43(12): 1-5. doi: 10.13718/j.cnki.xsxb.2018.12.001

引用本文:

钟琴¹,牟谷芳². 矩阵Hadamard积谱半径的新上界[J]. 西南师范大学学报(自然科学版), 2018, 43(12): 1-5. doi: 10.13718/j.cnki.xsxb.2018.12.001

ZHONG Qin1, MOU Gu-fang2. New Upper Bounds on the Spectral Radius for the Hadamard Product of Matrices[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(12): 1-5. doi: 10.13718/j.cnki.xsxb.2018.12.001

Citation:

ZHONG Qin¹, MOU Gu-fang². New Upper Bounds on the Spectral Radius for the Hadamard Product of Matrices[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(12): 1-5. doi: 10.13718/j.cnki.xsxb.2018.12.001

矩阵Hadamard积谱半径的新上界

钟琴¹,牟谷芳²

1. 四川大学锦江学院数学教学部, 四川彭山 620860;
2. 乐山师范学院数学与信息科学学院, 四川乐山 614000

New Upper Bounds on the Spectral Radius for the Hadamard Product of Matrices

ZHONG Qin¹, MOU Gu-fang²

1. Department of Mathematics, Jinjiang College of Sichuan University, Pengshan Sichuan 620860, China;
2. College of Mathematics and Information Science, Leshan Normal University, Leshan Sichuan 614000, China

摘要: 对于两个非负矩阵 A 和 B 的Hadamard积，利用特征值包含域定理给出谱半径的新上界估计式.数值例子表明新估计式在某些情况下比现有的估计式更为精确，并且这些估计式只依赖于两个非负矩阵的元素，更容易计算.
- 非负矩阵 /
- Hadamard积 /
- 谱半径 /
- 上界
Abstract: For the Hadamard product of two nonnegative matrices A and B , new upper bounds of the spectral radius have been given on the basis of the characteristic value containing domain theorems. The given numerical example show that these estimating formulas improve several existing results in some cases, and these bounds are easier calculate for they are only depending on the entries of nonnegative matrices.
- nonnegative matrix /
- Hadamard product /
- spectral radius /
- upper bound .

[1]	HORN R A, JOHNSON C R. Topics in Matrix Analysis[M]. 北京:人民邮电出版社, 2005.
[2]	FANG M Z. Bounds on Eigenvalues of Hadamard Product and the Fan Product of Matrices[J]. Linear Algebra Appl, 2007, 425(1):7-15.
[3]	HUANG R. Some Inequalities for the Hadamard Product and the Fan Product of Matrices[J]. Linear Algebra Appl, 2008, 428(7):1551-1559.
[4]	LIU Q B, CHEN G L. On Two Inequalities for the Hadamard Product and the Fan Product of Matrices[J]. Linear Algebra Appl, 2009, 431(5):974-984.
[5]	逄明贤. 矩阵谱论[M]. 长春:吉林大学出版社, 1989.
[6]	LI Y T, LI Y Y, WANG R W, et al. Some New Bounds on Eigenvalues of the Hadamard Product and the Fan Product of Matrices[J]. Linear Algebra Appl, 2010, 432:536-545.
[7]	LIU Q B, CHEN G L, ZHAO L L. Some New Bounds on the Spectral Radius of Matrices[J]. Linear Algebra Appl, 2010, 432(4):936-948.
[8]	GUO Q P, LI H B, SONG M Y. New Inequalities on Eigenvalues of the Hadamard Product and the Fan Product of Matrices[J]. J Inequal Appl, 2013, 2013(1):433-443.
[9]	HUANG Z G, XU Z, LU Q. Some New Estimations for the Upper and Lower Bounds for the Spectral Radius of Nonnegative Matrices[J]. J Inequal Appl, 2015, 2015(1):83-96.
[10]	CHEN F B, REN X H, HAO B. Some New Eigenvalue Bounds for the Hadamard Product and the Fan Product of Matrices[J]. 数学杂志, 2014, 34(5):895-903.
[11]	ZHAO L L. Two Inequalities for the Hadamard Product of Matrices[J]. J Inequal Appl, 2012, 2012(1):122-127.
[12]	CHENG G H, RAO X. Some Inequalities for the Spectral Radius of the Hadamard Product of Two Nonnegative Matrices[J]. J Math Inequal, 2013, 7(3):529-534.
[13]	CHENG G H. New Bounds for Eigenvalues of the Hadamard Product and the Fan Product of Matrices[J]. Taiwan J Math, 2014, 18(1):305-312.
[14]	孙德淑. 非负矩阵Hadamard的谱半径上界和M-矩阵Fan积的最小特征值下界的新估计[J]. 西南师范大学学报(自然科学版), 2016, 41(2):7-11.