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Some new inequalities involving the Hadamard product of an M-matrix and its inverse

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Abstract

For the Hadamard product of an M-matrix and its inverse, some new lower bounds on the minimum eigenvalue are given. These bounds can improve considerably some previous results.

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References

  1. Berman, A., Plemmons, R.J. Nonnegaive matrices in the mathematical sciences. Academic Press, New York, 1979

    MATH  Google Scholar 

  2. Chen, J.L. Special Matrix. Tsinghua University Press, Beijing, 2000

    Google Scholar 

  3. Chen, S.C. A lower bound for the minimum eigenvalue of the hadamard product of matrices. Linear Algebra Appl., 378: 159–166 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fiedler, M., Johnson, C.R., Markham, T., Neumann, M. A trace inequality for M-matrices and the symmetrizability of a real matrix by a positive diarix. Linear Algebra Appl., 71: 81–94 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fiedler, M., Markham, T. An inequality for the Hadamard product of an M-matrix and inverse M-matrix. Linear Algebra Appl., 101: 1–8 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  6. Horn, R.A., Johnson, C.R. Topics in Matrix Analysis. Cambridge University Press, Cambridge, 1985

    Book  MATH  Google Scholar 

  7. Li, H.B., Huang, T.Z., Shen, S.Q., Li, H. Lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse. Linnear Algebra Appl., 420: 235–247 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Li, Y.T., Chen, F.B., Wang, D.F. New lower bounds on eigenvalue of the Hadamard product of an M-matrix and its inverse. Linnear Algebra Appl., 430: 1423–1431 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Li, Y.T., Li, Y.Y., Wang, R.W., Wang, Y.Q. Some new lower bounds on eigenvalues of the Hadamard product and the Fan product of matrices. Linnear Algebra Appl., 432: 536–545 (2010)

    Article  MATH  Google Scholar 

  10. Li, Y.T., Liu, X., Yang, X.Y., Li, C.Q. Some new lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse. Electronic Journal of Linear Algebra, 22: 630–643 (2011)

    MathSciNet  MATH  Google Scholar 

  11. Song, Y.Z. On an inequality for the Hadamard product of an M-matrix and its inverse. Linnear Algebra Appl., 305: 99–105 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Varga, R.S. Minimal Gerschgorin sets. Pacific J. Math., 15 (2): 719–729 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  13. Xiang, S.H. On an inequality for the Hadamard product of an M-matrix or an H-matrix and its inverse. Linnear Algebra Appl., 367: 17–27 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Yong, X.R. Proof of a conjecture of Fiedler and Markham. Linnear Algebra Appl., 320: 167–171 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Yong, X.R., Wang, Z. On a conjecture of Fiedler and Markham. Linnear Algebra Appl., 288: 259–267 (1999)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors are very indebted to the referees for their valuable comments and corrections, which improved the original manuscript of this paper.

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Authors and Affiliations

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

    Feng Wang & Jian-xing Zhao

  2. School of Mathematics and Statistics, Yunnan University, Kunming, 650091, China

    Chao-qian Li

Authors
  1. Feng Wang
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  2. Jian-xing Zhao
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  3. Chao-qian Li
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Corresponding author

Correspondence to Feng Wang.

Additional information

Supported by National Natural Science Foundations of China (11361074, 11501141, 11601473) and CAS’ Light of West China’ Program.

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Wang, F., Zhao, Jx. & Li, Cq. Some new inequalities involving the Hadamard product of an M-matrix and its inverse. Acta Math. Appl. Sin. Engl. Ser. 33, 505–514 (2017). https://doi.org/10.1007/s10255-017-0678-x

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  • DOI: https://doi.org/10.1007/s10255-017-0678-x

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