关于矩阵的表示及其在熵中应用

doi:10.6040/j.issn.1671-9352.0.2020.424

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (11): 97-104.doi: 10.6040/j.issn.1671-9352.0.2020.424

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关于矩阵的表示及其在熵中应用

赵亚琪,任芳国^*

陕西师范大学数学与统计学院, 陕西西安 710062

发布日期:2021-11-15
作者简介:赵亚琪(1996— ),女,硕士研究生,研究方向为矩阵理论. E-mail:17864193469@163.com*通信作者简介:任芳国(1969— ),男,博士,副教授,硕士生导师,研究方向为矩阵理论及应用. E-mail:rfangguo@snnu.edu.cn
基金资助:
国家自然科学基金资助项目(11471200)

Representation of matrices and its applications to entropy

ZHAO Ya-qi, REN Fang-guo^*

School of Mathematics and Statistics, Shaanxi Normal University, Xian 710062, Shaanxi, China

Published:2021-11-15

摘要/Abstract

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。

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

Abstract: 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.

Key words: matrix entropy, concavity of entropy, density matrix, projection matrix, unitary similarity, probability distribution

中图分类号:

O151.21

赵亚琪,任芳国. 关于矩阵的表示及其在熵中应用[J]. 《山东大学学报(理学版)》, 2021, 56(11): 97-104.

ZHAO Ya-qi, REN Fang-guo. Representation of matrices and its applications to entropy[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(11): 97-104.

参考文献

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关于矩阵的表示及其在熵中应用

Representation of matrices and its applications to entropy

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