A mathematical review of the generalized entropies and their matrix trace inequalities

被引：0
|
作者：
Furuichi, Shigeru [1 ]
机构：
[1] Tokyo Univ Sci, Dept Elect & Comp Sci, Onoda, Yamaguchi 7560884, Japan
来源：
World Congress on Engineering 2007, Vols 1 and 2 | 2007年
关键词：
matrix trace inequalities; Tsallis relative entropy; Fannes' inequality; variational expression and maximum entropy principle;
D O I：
暂无
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
We review the properties of the generalized entropies in our previous papers in the following way. (1)A generalized Fannes' inequality is shown by the axiomatically characterized Tsallis entropy. (2)The maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for the non-negative matrices in the framework of matrix analysis. (3)A variational expression for Tsallis relative entropy is derived and some related inequalities are studied.
引用
收藏
页码：840 / 845
页数：6
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