Abstract
In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.
Similar content being viewed by others
References
R. B. Bapat and T. E. S. Ragharan: Nonnegative Matrices and Applications. Cambridge University Press, 1997.
R. B. Bapat and V. S. Sunder: On majorization and Schur products. Linear Algebra and its Applications 72 (1985), 107–117.
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.
R. A. Horn and C. R. Johnson: Topics in Matrix Analysis. Cambridge University Press, 1991.
A. W. Marshall and I. Olkin: Inequalities: Theory of Majorization and Its Applications. Academic Press, 1979.
L. Mirsky: An introduction to linear algebra. Oxford University, Oxford, 1955.
A. Oppenheim: Inequalities connected with definite Hermitian forms. J. London Math. Soc. 5 (1930), 114–119.
Author information
Authors and Affiliations
Corresponding author
Additional information
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).
Rights and permissions
About this article
Cite this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10587-009-0014-6