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The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices

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Abstract

In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.

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References

  1. R. B. Bapat and T. E. S. Ragharan: Nonnegative Matrices and Applications. Cambridge University Press, 1997.

  2. R. B. Bapat and V. S. Sunder: On majorization and Schur products. Linear Algebra and its Applications 72 (1985), 107–117.

    Article  MATH  MathSciNet  Google Scholar 

  3. S. M. Fallat and C. R. Johnson: Determinantal inequalities: ancient history and recent advances, Algebra and its Applications (Athens, OH, 1999), 199–212. Contemporary Math. 259, Amer. Math. Soc., Providence, RI, 2000.

    Google Scholar 

  4. R. A. Horn and C. R. Johnson: Topics in Matrix Analysis. Cambridge University Press, 1991.

  5. A. W. Marshall and I. Olkin: Inequalities: Theory of Majorization and Its Applications. Academic Press, 1979.

  6. L. Mirsky: An introduction to linear algebra. Oxford University, Oxford, 1955.

    MATH  Google Scholar 

  7. A. Oppenheim: Inequalities connected with definite Hermitian forms. J. London Math. Soc. 5 (1930), 114–119.

    Article  Google Scholar 

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Correspondence to Xiao-Dong Zhang.

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Supported by National Natural Science Foundation of China (No. 10531070), National Basic Research Program of China 973 Program (No. 2006CB805900), National Research Program of China 863 Program (No. 2006AA11Z209) and the Natural Science Foundation of Shanghai (Grant No. 06ZR14049).

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Zhang, XD., Ding, CX. The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices. Czech Math J 59, 197–206 (2009). https://doi.org/10.1007/s10587-009-0014-6

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  • DOI: https://doi.org/10.1007/s10587-009-0014-6

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