{"title":"什么时候每个线性变换都是幂q变换和局部幂零变换的和？","authors":"A.N. Abyzov, D.T. Tapkin","doi":"10.1016/j.laa.2025.01.012","DOIUrl":null,"url":null,"abstract":"<div><div>We prove that for each vector space <em>V</em> over <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span>, every linear transformation of <em>V</em> is a sum of a <em>q</em>-potent linear transformation and a locally nilpotent linear transformation.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"709 ","pages":"Pages 124-131"},"PeriodicalIF":1.1000,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"When is every linear transformation a sum of a q-potent one and a locally nilpotent one?\",\"authors\":\"A.N. Abyzov, D.T. Tapkin\",\"doi\":\"10.1016/j.laa.2025.01.012\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We prove that for each vector space <em>V</em> over <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span>, every linear transformation of <em>V</em> is a sum of a <em>q</em>-potent linear transformation and a locally nilpotent linear transformation.</div></div>\",\"PeriodicalId\":18043,\"journal\":{\"name\":\"Linear Algebra and its Applications\",\"volume\":\"709 \",\"pages\":\"Pages 124-131\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2025-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Linear Algebra and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0024379525000126\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2025/1/13 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Algebra and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0024379525000126","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/13 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
When is every linear transformation a sum of a q-potent one and a locally nilpotent one?
We prove that for each vector space V over , every linear transformation of V is a sum of a q-potent linear transformation and a locally nilpotent linear transformation.
期刊介绍：
Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.
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