Decompositions of matrices into a sum of invertible matrices and matrices of fixed nilpotence

IF 0.7 4区 数学 Q2 Mathematics
P. Danchev, E. García, M. Gómez Lozano
{"title":"Decompositions of matrices into a sum of invertible matrices and matrices of fixed nilpotence","authors":"P. Danchev, E. García, M. Gómez Lozano","doi":"10.13001/ela.2023.7851","DOIUrl":null,"url":null,"abstract":"For any $n\\ge 2$ and fixed $k\\ge 1$, we give necessary and sufficient conditions for an arbitrary nonzero square matrix in the matrix ring $\\mathbb{M}_n(\\mathbb{F})$ to be written as a sum of an invertible matrix $U$ and a nilpotent matrix $N$ with $N^k=0$ over an arbitrary field $\\mathbb{F}$.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-08-24","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.2023.7851","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

Abstract

For any $n\ge 2$ and fixed $k\ge 1$, we give necessary and sufficient conditions for an arbitrary nonzero square matrix in the matrix ring $\mathbb{M}_n(\mathbb{F})$ to be written as a sum of an invertible matrix $U$ and a nilpotent matrix $N$ with $N^k=0$ over an arbitrary field $\mathbb{F}$.
矩阵分解为可逆矩阵和固定幂零矩阵的和
对于任意$n\ge 2$和固定$k\ge 1$,我们给出了矩阵环$\mathbb{M}_n(\mathbb{F})$中的任意非零方阵在任意域$\mathbb{F}$上写成可逆矩阵$U$与n ^k=0$的幂零矩阵$n $的和的充要条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信