本文選題：冪等算子　切入點(diǎn)：廣義逆　出處：《湖北師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：冪等算子和矩陣的廣義逆問(wèn)題是矩陣?yán)碚撝惺种匾难芯空n題.近年來(lái),中外學(xué)者就各種特殊矩陣及組合的廣義逆作了很多的研究.本文中運(yùn)用矩陣空間分解及M-C-S分解的方法研究了兩個(gè)冪等算子組合在不同條件下的逆、群逆和Core逆等廣義逆的存在性問(wèn)題,并給出該冪等算子組合的廣義逆計(jì)算公式.內(nèi)容安排如下:第一章主要介紹本文寫(xiě)作背景及需要用的符號(hào)等.第二章首先介紹兩個(gè)冪等算子組合的逆存在的充要條件,然后給出了在滿足不同條件下的冪等算子組合逆的表達(dá)式.第三章首先介紹群逆的基本概念及性質(zhì),然后研究了在滿足不同條件下的冪等算子組合的群逆的存在性及其表達(dá)式問(wèn)題.第四章首先介紹Core逆的基本概念及性質(zhì),然后研究了兩個(gè)冪等算子組合的Core逆的存在性及其表達(dá)式問(wèn)題.
[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.
【學(xué)位授予單位】：湖北師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O151.21

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本文編號(hào)：1576650