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

Xiao-Dong Zhang; Chang-Xing Ding

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 1, page 197-206
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Zhang, Xiao-Dong, and Ding, Chang-Xing. "The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices." Czechoslovak Mathematical Journal 59.1 (2009): 197-206. <http://eudml.org/doc/37917>.

@article{Zhang2009,
abstract = {In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.},
author = {Zhang, Xiao-Dong, Ding, Chang-Xing},
journal = {Czechoslovak Mathematical Journal},
keywords = {Oppenheim's inequality; Schur's inequality; positive semidefinite matrix; Hadamard product; Oppenheim's inequality; Schur's inequality; positive semidefinite matrix; Hadamard product},
language = {eng},
number = {1},
pages = {197-206},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices},
url = {http://eudml.org/doc/37917},
volume = {59},
year = {2009},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 197
EP - 206
AB - In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.
LA - eng
KW - Oppenheim's inequality; Schur's inequality; positive semidefinite matrix; Hadamard product; Oppenheim's inequality; Schur's inequality; positive semidefinite matrix; Hadamard product
UR - http://eudml.org/doc/37917
ER -

References

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  1. Bapat, R. B., Ragharan, T. E. S., Nonnegative Matrices and Applications, Cambridge University Press (1997). (1997) MR1449393
  2. Bapat, R. B., Sunder, V. S., On majorization and Schur products, Linear Algebra and its Applications 72 (1985), 107-117. (1985) Zbl0577.15016MR0815257
  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). (2000) MR1778502
  4. Horn, R. A., Johnson, C. R., Topics in Matrix Analysis, Cambridge University Press (1991). (1991) Zbl0729.15001MR1091716
  5. Marshall, A. W., Olkin, I., Inequalities: Theory of Majorization and Its Applications, Academic Press (1979). (1979) Zbl0437.26007MR0552278
  6. Mirsky, L., An introduction to linear algebra, Oxford University, Oxford (1955). (1955) Zbl0066.26305MR0074364
  7. Oppenheim, A., 10.1112/jlms/s1-5.2.114, J. London Math. Soc. 5 (1930), 114-119. (1930) MR1574213DOI10.1112/jlms/s1-5.2.114

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