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Some New Bounds for the Eigenvalues of Hadamard Product of Two Irreducible M-matrices

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 154)

Abstract

To study the lower bound for the minimum eigenvalue and a upper bound for the spectral radius of Hadamard product of two irreducible M-matrices A and B , obtaining some new estimation of the bounds. These new bounds are only depend on the element of A and B, so they are easy to calculate.

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References

  1. 1.
    M. Fiedler, T.L. Markham, An inequality for the Hadamard product of an M-matrix, Linear Algebra Appl. 101 (1988) 1–8.Google Scholar
  2. 2.
    M. Fiedler, C.R. Johnson, T.L. Markham, M. Neumann, A trace inequality for M - matrices and the symmetrizability of a real matrix by a positive diagonal matrix, Linear Algebra Appl. 71 (1985) 81–94.Google Scholar
  3. 3.
    X.R. Yong, Proof of a conjecture of Fiedler and Markham. Linear Algebra Appl. 320 (2000) 167–171.Google Scholar
  4. 4.
    Y.Z. Song, On an inequality for the Hadamard product of an M-matrix, Linear Algebra Appl. 305 (2000) 99–105.Google Scholar
  5. 5.
    S.C. Chen, A lower bound for the minimum eigenvalue of the Hadamard product of matrix, Linear Algebra Appl. 378 (2004) 159–166.Google Scholar
  6. 6.
    H.B. Li, T.Z. Huang, S.Q. Shen, H. Li, Lower bounds for the eigenvalue of Hadamard product of an M-matrix and its inverse, Linear Algebra Appl. 420 (2007) 235–247.Google Scholar
  7. 7.
    Y.T. Li, F.B. Chen, D.F. Wang, New lower bounds on eigenvalue of the Hadamard product of an M -matrix and its inverse, Linear Algebra Appl. 430(2009)1423–1431.Google Scholar
  8. 8.
    Y.T. Li, Y.Y. Li, R.W. Wang, Y.Q. Wang, Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices, Linear Algebra Appl. 432(2010)536–545.Google Scholar
  9. 9.
    R.S. Varga, Minimal Gerschgorin sets, Pacific J. Math. 15(2) (1965) 719–729.Google Scholar
  10. 10.
    X.R. Yong, Z. Wang, On a a conjecture of Fiedler and Markham, Linear Algebra Appl. 288(1999)259–267.Google Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.The College of Humanities and SciencesGuizhou University for NationalitiesGuizhouChina

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