The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 197-206

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In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.
In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.
Classification : 15A45, 15A57
Keywords: Oppenheim's inequality; Schur's inequality; positive semidefinite matrix; Hadamard product
Zhang, Xiao-Dong; Ding, Chang-Xing. The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 197-206. http://geodesic.mathdoc.fr/item/CMJ_2009_59_1_a13/
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     year = {2009},
     volume = {59},
     number = {1},
     mrnumber = {2486625},
     zbl = {1224.15042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_1_a13/}
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[1] Bapat, R. B., Ragharan, T. E. S.: Nonnegative Matrices and Applications. Cambridge University Press (1997). | MR

[2] Bapat, R. B., Sunder, V. S.: On majorization and Schur products. Linear Algebra and its Applications 72 (1985), 107-117. | MR | Zbl

[3] Fallat, S. M., Johnson, C. R.: 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). | MR

[4] Horn, R. A., Johnson, C. R.: Topics in Matrix Analysis. Cambridge University Press (1991). | MR | Zbl

[5] Marshall, A. W., Olkin, I.: Inequalities: Theory of Majorization and Its Applications. Academic Press (1979). | MR | Zbl

[6] Mirsky, L.: An introduction to linear algebra. Oxford University, Oxford (1955). | MR | Zbl

[7] Oppenheim, A.: Inequalities connected with definite Hermitian forms. J. London Math. Soc. 5 (1930), 114-119. | DOI | MR