两个幂等算子组合的广义逆

发布时间：2018-03-06 22:00

本文选题：幂等算子　切入点：广义逆　出处：《湖北师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：幂等算子和矩阵的广义逆问题是矩阵理论中十分重要的研究课题.近年来,中外学者就各种特殊矩阵及组合的广义逆作了很多的研究.本文中运用矩阵空间分解及M-C-S分解的方法研究了两个幂等算子组合在不同条件下的逆、群逆和Core逆等广义逆的存在性问题,并给出该幂等算子组合的广义逆计算公式.内容安排如下:第一章主要介绍本文写作背景及需要用的符号等.第二章首先介绍两个幂等算子组合的逆存在的充要条件,然后给出了在满足不同条件下的幂等算子组合逆的表达式.第三章首先介绍群逆的基本概念及性质,然后研究了在满足不同条件下的幂等算子组合的群逆的存在性及其表达式问题.第四章首先介绍Core逆的基本概念及性质,然后研究了两个幂等算子组合的Core逆的存在性及其表达式问题.
[Abstract]:The generalized inverse problem of idempotent operators and matrices is a very important research topic in matrix theory. Chinese and foreign scholars have done a lot of research on the generalized inverse of various special matrices and combinations. In this paper, the inverse of the combination of two idempotent operators under different conditions is studied by using the methods of matrix space decomposition and M-C-S decomposition. The existence of generalized inverses such as group inverse and Core inverse, The general inverse formula of the combination of idempotent operators is given. The contents are arranged as follows: chapter 1 mainly introduces the background of this paper and the symbols that need to be used. Chapter 2 introduces the necessary and sufficient conditions for the inverse existence of the combination of two idempotent operators. Then the expression of the combination inverse of idempotent operators under different conditions is given. In chapter 3, the basic concepts and properties of group inverse are introduced. Then we study the existence and expression of group inverse of the combination of idempotent operators under different conditions. Chapter 4th first introduces the basic concept and properties of Core inverse. Then we study the existence and expression of Core inverse of two idempotent operators combination.
【学位授予单位】：湖北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O151.21

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