Entropy functions and determinant inequalities

机译：熵函数和行列式不等式

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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 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 × 3 positive definite matrices are completely characterized by Shannon-type information inequalities.

机译：在本文中，我们表明，n×n个正定矩阵的所有行列式不等式的特征等同于确定包含由n个标量联合高斯随机变量引起的所有熵函数的最小闭合锥面和凸锥面。通过使用可表示的函数和熵函数，我们获得了圆锥上的内部和外部边界。特别是，对于n≤3，这些边界是紧的和明确的，这意味着3×3正定矩阵的行列式不等式完全由Shannon型信息不等式表征。

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来源
《2012 IEEE International Symposium on Information Theory Proceedings》|2012年|p.1251- 1255|共5页
会议地点 Cambridge MA(US)
作者
Chan Terence; Guo Dongning; Yeung Raymond;
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作者单位

Institute of Telecom. Research, University of South Australia;

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会议组织
原文格式 PDF
正文语种 eng
中图分类通信理论;
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Entropy functions and determinant inequalities

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