关于矩阵分解为对合对易子积的问题

IF 0.7 4区数学 Q2 Mathematics Electronic Journal of Linear Algebra Pub Date : 2022-02-23 DOI:10.13001/ela.2022.6797

Tran Nam Son, Truong Huu Dung, Nguyen Thi Thai Ha, Mai Hoang Bien

{"title":"关于矩阵分解为对合对易子积的问题","authors":"Tran Nam Son, Truong Huu Dung, Nguyen Thi Thai Ha, Mai Hoang Bien","doi":"10.13001/ela.2022.6797","DOIUrl":null,"url":null,"abstract":"Let $F$ be a field and let $n$ be a natural number greater than $1$. The aim of this paper is to prove that if $F$ contains at least three elements, then every matrix in the special linear group $\\mathrm{SL}_n(F)$ is a product of at most two commutators of involutions.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"On decompositions of matrices into products of commutators of involutions\",\"authors\":\"Tran Nam Son, Truong Huu Dung, Nguyen Thi Thai Ha, Mai Hoang Bien\",\"doi\":\"10.13001/ela.2022.6797\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $F$ be a field and let $n$ be a natural number greater than $1$. The aim of this paper is to prove that if $F$ contains at least three elements, then every matrix in the special linear group $\\\\mathrm{SL}_n(F)$ is a product of at most two commutators of involutions.\",\"PeriodicalId\":50540,\"journal\":{\"name\":\"Electronic Journal of Linear Algebra\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-02-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Linear Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.13001/ela.2022.6797\",\"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.2022.6797","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: 4

摘要

设$F$是一个字段，设$n$是大于$1$的自然数。本文的目的是证明如果$F$至少包含三个元素，则特殊线性群$\mathrm中的每个矩阵{SL}_n（F） $是对合的至多两个交换子的乘积。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

On decompositions of matrices into products of commutators of involutions

Let $F$ be a field and let $n$ be a natural number greater than $1$. The aim of this paper is to prove that if $F$ contains at least three elements, then every matrix in the special linear group $\mathrm{SL}_n(F)$ is a product of at most two commutators of involutions.

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.