关于矩阵的表示及其在熵中应用  

Representation of matrices and its applications to entropy

作　　者：赵亚琪 任芳国[1] ZHAO Ya-qi;REN Fang-guo(School of Mathematics and Statistics,Shaanxi Normal University,Xian 710062,Shaanxi,China)

机构地区：[1]陕西师范大学数学与统计学院,陕西西安710062

出　　处：《山东大学学报（理学版）》2021年第11期97-104,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11471200)。

摘　　要：研究了矩阵酉相似概率分布表示的特性及矩阵熵凹性的应用。通过对分块矩阵、投影矩阵及矩阵熵的凹性进行研究,获得了任意方阵的酉相似概率分布的特性、任意密度矩阵关于一组完备正交投影矩阵变换的酉相似概率分布表示及矩阵熵的若干不等式。To study the properties about the representation for probabilistic distribution of unitary similarities of a matrix and the applications about the concavity of matrix entropy, some research about block matrix, projection matrix and the concavity of matrix entropy is studied. The probabilistic distribution of unitary similarities of any square matrix, the representation of the probabilistic distribution of unitary similarities for the transformation about a complete set of orthogonal projection matrix of any density matrix and some inequalities of matrix entropy are obtained.

关 键 词：矩阵熵 熵的凹性 密度矩阵 投影矩阵 酉相似 概率分布 

分 类 号：O151.21[理学—数学]