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Research Article

An Oppenheim type inequality for positive definite block matrices

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Pages 4455-4466 | Received 03 May 2020, Accepted 22 Jan 2021, Published online: 09 Feb 2021

References

  • Agaian SS. Hadamard matrices and their applications. Berlin: Springer-Verlag; 1985.
  • Ando T. Inequalities for M–matrices. Linear Multilinear Algebra. 1980;8:291–316.
  • Chen S. Some determinantal inequalities for Hadamard product of matrices. Linear Algebra Appl. 2003;368:99–106.
  • Chen S. Inequalities for M–matrices and inverse M–matrices. Linear Algebra Appl. 2007;426:610–618.
  • Choi D. Inequalities related to trace and determinant of positive semidefinite block matrices. Linear Algebra Appl. 2017;532:1–7.
  • Dong S, Li Q. Extension of an Oppenheim type determinantal inequality for the block Hadamard product. Math Inequal Appl. 2020;23(2):539–545.
  • Fu X, Liu Y. Some determinantal inequalities for Hadamard and Fan products of matrices. J Inequal Appl. 2016;2016:262–269.
  • Günther M, Klotz L. Schur's theorem for a block Hadamard product. Linear Algebra Appl. 2012;437:948–956.
  • Gunus M, Liu J, Raouafi S, et al. Positive semi-definite 2 × 2 block matrices and norm inequalities. Linear Algebra Appl. 2018;551:83–91.
  • Hedayat A, Wallis WD. Hadamard matrices and their applications. Ann Stat. 1978;6:1184–1238.
  • Horn RA, Mathias R, Nakamura Y. Inequalities for unitarily invariant norms and bilinear matrix products. Linear Multilinear Algebra. 1991;30:303–314.
  • Horn RA, Johnson CR. Matrix analysis. 2nd ed. Cambridge University Press; 2013.
  • Kim S, Kim J, Lee H. Oppenheim and Schur type inequalities for Khatri-Rao product of positive definite matrices. Kyungpook Math J. 2017;57:133–144.
  • Kittaneh F, Lin M. Trace inequalities for positive semidefinite block matrices. Linear Algebra Appl. 2017;524:153–158.
  • Liu J, Zhu L. Some improvement of Oppenheim's inequality for M–matrices. SIAM J Matrix Anal Appl. 1997;18(2):305–311.
  • Lin M. An Oppenheim type inequality for a block Hadamard product. Linear Algebra Appl. 2014;452:1–6.
  • Lin M. A determinantal inequality involving partial traces. Can Math Bull. 2016;59:585–591.
  • Lin M, Zhang P. Unifying a result of Thompson and a result of Fiedler and Markham on block positive definite matrices. Linear Algebra Appl. 2017;533:380–385.
  • Oppenheim A. Inequalities connected with definite Hermitian forms. J London Math Soc. 1930;5:114–119.
  • Seberry J, Yamada M. Hadamard matrices, sequences, and block designs. In: Dinitz JH, Stinson DR, editors. Contemporary design theory: a collection of surveys. New York (NY): John Wiley Sons; 1992. Chap. 11.
  • Styan GPH. Hadamard products and multivariate statistical analysis. Linear Algebra Appl. 1973;6:217–240.
  • Yang Z, Liu J. Some results on Oppenheim's inequalities for M–matrices. SIAM J Matrix Anal Appl. 2000;21(3):904–912.
  • Zhang X-D. The equality cases for the inequalities of Fischer, Oppenheim, and Ando for general M-matrices. SIAM J Matrix Anal Appl. 2004;25(3):752–765.
  • Zhang X-D, Ding C-X. The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices. Czech Math J. 2009;59:197–206.
  • Zhang F. The schur complement and its applications. New York (NY): Springer; 2005.
  • Zhang F. Matrix theory: basic results and techniques. 2nd ed. New York (NY): Springer; 2011.
  • Zhang P. On some inequalities related to positive block matrices. Linear Algebra Appl. 2019;576:258–267.

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