Corpus ID: 119138437

Logarithmic inequalities under an elementary symmetric polynomial dominance order

@article{Sra2015LogarithmicIU,
  title={Logarithmic inequalities under an elementary symmetric polynomial dominance order},
  author={S. Sra},
  journal={arXiv: Classical Analysis and ODEs},
  year={2015}
}
  • S. Sra
  • Published 2015
  • Mathematics, Physics
  • arXiv: Classical Analysis and ODEs
  • We consider a dominance order on positive vectors induced by the elementary symmetric polynomials. Under this dominance order we provide conditions that yield simple proofs of several monotonicity questions. Notably, our approach yields a quick (4 line) proof of the so-called \emph{"sum-of-squared-logarithms"} inequality conjectured in (P.~Neff, B.~Eidel, F.~Osterbrink, and R.~Martin, \emph{Applied Math. \& Mechanics., 2013}; P.~Neff, Y.~Nakatsukasa, and A.~Fischle; \emph{SIMAX, 35, 2014… CONTINUE READING

    References

    SHOWING 1-10 OF 12 REFERENCES
    The sum of squared logarithms inequality in arbitrary dimensions
    • 16
    • PDF
    Symmetric polynomials in information theory: entropy and subentropy
    • 14
    • Highly Influential
    • PDF
    Positive definite matrices and the S-divergence
    • 82
    • PDF
    Inequalities: Theory of Majorization and Its Applications
    • 5,852
    • PDF
    Positive Definite Matrices
    • 1,194
    • PDF
    Matrix analysis
    • 27,814
    • PDF
    On the generalised sum of squared logarithms inequality
    • 8
    • PDF