2012/01/25 by Chan, Terence, Guo, Dongning, Yeung, Raymond
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1201.5241
In this paper, we show that the characterisation of all determinant inequalities for n × n positive definite matrices is equivalent to determining the smallest closed and convex cone containing all entropy functions induced by n scalar 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 × 3 positive definite matrices are completely characterized by Shannon-type information inequalities.