对称非奇异矩阵的α-对偶几何结构（英文）

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英文篇名：The α-dual Differential Geometry of Symmetric Nonsingular Matrices 作者：吴利萍 ; 张绍祥 英文作者：Wu Liping;Zhang Shaoxiang;College of Science,Tianjin University of Technology;School of Mathematical Sciences,Nankai University; 关键词：统计流形 ; 对称非奇异矩阵 ; α-对偶联络 英文关键词：statistical manifold;;symmetric nonsingular matrix;;α-dual connections 中文刊名：NKDZ 英文刊名：Acta Scientiarum Naturalium Universitatis Nankaiensis 机构：天津理工大学理学院;南开大学数学科学学院; 出版日期：2019-06-15 出版单位：南开大学学报(自然科学版) 年：2019 期：v.52 语种：英文; 页：NKDZ201903016 页数：5 CN：03 ISSN：12-1105/N 分类号：92-96

摘要

研究了由所有对称非奇异n阶矩阵构成的流形S (n),在S (n)上定义了合理的黎曼度量并由此得到α-对偶联络,进一步得到S (n)的α-对偶几何结构,然后给出了具体例子.
        The manifold S(n) is explored. The set of all symmetric nonsingular matrices on which a Riemannian metric is defined and dual α-connections are introduced. Furthermore, the α-dual geometric structure is obtained. Finally, an example is given to illustrate our results.

引文

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