Entropy functions and determinant inequalities

Terence Chan*, Dongning Guo, Raymond Yeung

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

In this paper, we show that the characterisation of all determinant inequalities for n x n positive definite matrices is equivalent to determining the smallest closed and convex cone containing all entropy functions induced by n scalar jointly Gaussian random variables. We have obtained inner and outer bounds on the cone by using representable functions and entropic functions. In particular, these bounds are tight and explicit for n ≤ 3, implying that determinant inequalities for 3 x 3 positive definite matrices are completely characterized by Shannon-type information inequalities.

Original languageEnglish (US)
Title of host publication2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012
Pages1251-1255
Number of pages5
DOIs
StatePublished - Oct 22 2012
Event2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States
Duration: Jul 1 2012Jul 6 2012

Other

Other2012 IEEE International Symposium on Information Theory, ISIT 2012
CountryUnited States
CityCambridge, MA
Period7/1/127/6/12

Keywords

  • Entropy
  • Gaussian distribution
  • rank functions

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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    Chan, T., Guo, D., & Yeung, R. (2012). Entropy functions and determinant inequalities. In 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012 (pp. 1251-1255). [6283057] https://doi.org/10.1109/ISIT.2012.6283057