华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (5): 45-50.

• 应用数学,统计学 • 上一篇    下一篇

矩阵Hadamard积和Fan积特征值的界

杜琨   

  1. 华东师范大学数学系,上海200062
  • 收稿日期:2007-11-02 修回日期:2008-01-10 出版日期:2008-09-25 发布日期:2008-09-25
  • 通讯作者: 杜琨

Bounds for eigenvalues of Hadamard product and Fan product of matrices (Chinese)

DU Kun   

  1. Department of Mathematics, East China Normal University, Shanghai 200062; China
  • Received:2007-11-02 Revised:2008-01-10 Online:2008-09-25 Published:2008-09-25
  • Contact: DU Kun

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摘要： 利用Cauchy--Schwitz不等式给出两个n阶非负矩阵A和B的Hadamard积A。B的谱半径ρ(A。B)的一组上界;并且与前人给出的结果进行比较,从而说明新结果的创新之处.类似地,利用Cauchy--Schwitz不等式给出两个n阶M--方阵A和B的Fan积A★B的最小特征值т(A★B)的一组下界.

关键词: Hadamard积, Fan积, M--方阵, 谱半径, 最小特征值, Hadamard积, Fan积, M--方阵, 谱半径, 最小特征值

Abstract: This paper found a new type upper bound of ρ(A。B) which was the spectral radius of the Hadamard product of two nonnegative matrices A and B by using Cauchy—Schwitz inequality and compared the new type upper bound with the classical results. In the same way, this paper found a new type lower bound of т(A★B),which was the minimum eigenvalue of the Fan product of two M--matrices A and B.

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

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