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两个矩阵Fan积和Hadamard积的特征值的界 被引量：1

Bounds on Eigenvalues of the Fan Product and the Hadamard Product of Two Matrices
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摘要 关于非奇异M-矩阵A与B的Fan积A*B,给出A*B的最小特征值τ(A*B)下界的新估计式,同时也给出非负矩阵A与B的Hadamard积A○B的谱半径ρ(A○B)上界的新估计式,这些估计式只与矩阵的元素有关,易于计算.数值算例也说明所得估计式改进了现有的结果. If A and B are nonsingular -matrices,a new lower bound on the minimum eigenvalue for the Fan product of A and B and new upper bounds on the spectral radius of nonnegative matrces A and B are given in the paper. The bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they only depend on the entries of matrices A and B.
作者 杨晓英 刘新
机构地区 四川信息职业技术学院基础教育部
出处 《文山学院学报》 2012年第3期31-35,共5页 Journal of Wenshan University
关键词 M-矩阵 非负矩阵 Fan积 HADAMARD积 最小特征值 谱半径 Matrix normegative matrix Fan product Hadamard product minimum eigenvalue spectral radius
分类号 O151.21 [理学—基础数学]
  • 相关文献

参考文献8

  • 1Horn R A, Johnson C R. Topics in matrix analysis [ M ] . New York: Cambridge University Press, 1991: 129, 131, 358-359.
  • 2陈景良,陈向晖.特殊矩阵[M].北京:清华大学出版社,2000.130.
  • 3Fang M Z. Bounds on eigenvalues of the Hadamard product and the Fan product of matrices J ]. Linear Algebra Appl, 2007, 425: 7-15.
  • 4Huang R. Some inequalities for the Hadamard product and the Fan product of matrices E J ] Linear Algebra Appl, 2008, 428 1551-1559.
  • 5Liu Q B, Chen G L. On two inequalities for the Hadamard product and the Fan product of matrices [ J ] . Linear Algebra Appl, 2009, 431: 974-984.
  • 6Li 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李艳艳,李耀堂.矩阵Hadamard积和Fan积的特征值界的估计[J].云南大学学报（自然科学版）,2010,32(2):125-129. 被引量：20
  • 8Berman A, Plemmons R J. Nonnegative Matrices in the Mathematical Sciences [ M ] . New York: Academic Press, 1979: 26-27.

二级参考文献10

  • 1孙丽英,许兴业.H-矩阵的刻化及一类实矩阵逆的上下界估计[J].云南大学学报（自然科学版）,2005,27(4):285-288. 被引量：2
  • 2HORN R A,JOHNSON C R. Topics in matrix analysis [ M ]. New York:Cambridge University Press, 1991.
  • 3BERMAN A, PLEMONS R J. Nonnegative matrices in the mathematical sciences[ M ]. New York:Academic Press, 1979.
  • 4HORN R A,JOHNSON C R. Topics in matrix analysis[ M]. New York:Cambridge University Press, 1985.
  • 5FANG M Z. Bounds on eigenvalue of the Hadamard product and the Fan product of matrices[J]. Linear Algebra Appl,2007,425:7-15.
  • 6HUANG R. Some inequalities for the Hadamard product and Fan product of matrices [ J ]. Linear Algebra Appl,2008,428: 1 551-1 559.
  • 7LIU Q B,CHEN G L. On two inequalities for the Hadamard product and Fan product of matrices [ J ]. Linear Algebra Appl, 2009.03. 049. doi : 10. 1016/j. laa.
  • 8游兆永.非奇异M-矩阵[M].武汉:武汉工学院出版社,1981.
  • 9陈景良,陈向晖.特殊矩阵[M].北京:清华大学出版社,2000.130.
  • 10袁晖坪.关于行(列)反对称矩阵的Schur分解[J].云南大学学报（自然科学版）,2008,30(6):549-552. 被引量：2

共引文献82

同被引文献8

  • 1陈景良,陈向晖.特殊矩阵[M].北京:清华大学出版社,2000.130.
  • 2Hom R A,Johnson C R.Topics in matrix analysis[M]. New York:Cambridge University Press,1991.
  • 3Fang M Z. Bounds on eigenvalues of the Hadamard prod- uct and the Fan product of matrices [J]. Linear Algebra Appl. 2007,425:7-15.
  • 4Huang R. Some inequalities for the Hadamard product and the Fan product of matrices [J]. Linear Algebra Appl.,2008,428:1551-1559.
  • 5Liu Q B, Chen G L. On two inequalities for the Had- amard product and the Fan product of matrices[J].Linear Algebra Appl.,2009,431:974-984.
  • 6Brauer A.Limits for the characteristic roots of a matrix Ⅱ [J].Duke Math.,J. 1947,14:21-26.
  • 7Li Y T,Li Y Y,Wang R W, et al.Some new bounds on eigenvalues of the Hadamard product and the Fan prod- uct of matrices [J]. Linear Algebra Appl. ,2010,432:536- 545.
  • 8Vargar S. Minimal Gerschgorin sets [J]. Pacific J. Math., 1965,15 (2):719-729.

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文山学院学报
2012年 第3期

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