Keywords: Oppenheim's inequality; Schur's inequality; positive semidefinite matrix; Hadamard product
@article{CMJ_2009_59_1_a13,
author = {Zhang, Xiao-Dong and Ding, Chang-Xing},
title = {The equality cases for the inequalities of {Oppenheim} and {Schur} for positive semi-definite matrices},
journal = {Czechoslovak Mathematical Journal},
pages = {197--206},
year = {2009},
volume = {59},
number = {1},
mrnumber = {2486625},
zbl = {1224.15042},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_1_a13/}
}
TY - JOUR AU - Zhang, Xiao-Dong AU - Ding, Chang-Xing TI - The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices JO - Czechoslovak Mathematical Journal PY - 2009 SP - 197 EP - 206 VL - 59 IS - 1 UR - http://geodesic.mathdoc.fr/item/CMJ_2009_59_1_a13/ LA - en ID - CMJ_2009_59_1_a13 ER -
%0 Journal Article %A Zhang, Xiao-Dong %A Ding, Chang-Xing %T The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices %J Czechoslovak Mathematical Journal %D 2009 %P 197-206 %V 59 %N 1 %U http://geodesic.mathdoc.fr/item/CMJ_2009_59_1_a13/ %G en %F CMJ_2009_59_1_a13
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/
[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