极小秩弱Drazin逆：一类具有指定范围的外逆

IF 0.7 4区数学 Q2 Mathematics

Electronic Journal of Linear Algebra Pub Date : 2023-02-09 DOI:10.13001/ela.2023.7359

Cang Wu, Jianlong Chen

{"title":"极小秩弱Drazin逆：一类具有指定范围的外逆","authors":"Cang Wu, Jianlong Chen","doi":"10.13001/ela.2023.7359","DOIUrl":null,"url":null,"abstract":"For any square matrix $A$, it is proved that minimal rank weak Drazin inverses (Campbell and Meyer, 1978) of $A$ coincide with outer inverses of $A$ with range $\\mathcal{R}(A^{k})$, where $k$ is the index of $A$. It is shown that the minimal rank weak Drazin inverse behaves very much like the Drazin inverse, and many generalized inverses such as the core-EP inverse and the DMP inverse are its special cases.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Minimal rank weak Drazin inverses: a class of outer inverses with prescribed range\",\"authors\":\"Cang Wu, Jianlong Chen\",\"doi\":\"10.13001/ela.2023.7359\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For any square matrix $A$, it is proved that minimal rank weak Drazin inverses (Campbell and Meyer, 1978) of $A$ coincide with outer inverses of $A$ with range $\\\\mathcal{R}(A^{k})$, where $k$ is the index of $A$. It is shown that the minimal rank weak Drazin inverse behaves very much like the Drazin inverse, and many generalized inverses such as the core-EP inverse and the DMP inverse are its special cases.\",\"PeriodicalId\":50540,\"journal\":{\"name\":\"Electronic Journal of Linear Algebra\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-02-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Linear Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.13001/ela.2023.7359\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Linear Algebra","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.13001/ela.2023.7359","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

对于任意方阵$A$，证明了$A$的最小秩弱Drazin逆(Campbell and Meyer, 1978)与$A$的外逆在$\mathcal{R}(A^{k})$范围内一致，其中$k$是$A$的索引。证明了极小阶弱Drazin逆的性质与Drazin逆非常相似，许多广义逆如core-EP逆和DMP逆都是它的特例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Minimal rank weak Drazin inverses: a class of outer inverses with prescribed range

For any square matrix $A$, it is proved that minimal rank weak Drazin inverses (Campbell and Meyer, 1978) of $A$ coincide with outer inverses of $A$ with range $\mathcal{R}(A^{k})$, where $k$ is the index of $A$. It is shown that the minimal rank weak Drazin inverse behaves very much like the Drazin inverse, and many generalized inverses such as the core-EP inverse and the DMP inverse are its special cases.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Electronic Journal of Linear Algebra 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.