{"title":"代数闭域和有限域上矩阵的若干分解","authors":"P. Danchev","doi":"10.17516/1997-1397-2021-14-5-547-553","DOIUrl":null,"url":null,"abstract":"We study when every square matrix over an algebraically closed field or over a finite field is decomposable into a sum of a potent matrix and a nilpotent matrix of order 2. This can be related to our recent paper, published in Linear & Multilinear Algebra (2022). We also completely address the question when each square matrix over an infinite field can be decomposed into a periodic matrix and a nilpotent matrix of order 2","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"9 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On Some Decompositions of Matrices over Algebraically Closed and Finite Fields\",\"authors\":\"P. Danchev\",\"doi\":\"10.17516/1997-1397-2021-14-5-547-553\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study when every square matrix over an algebraically closed field or over a finite field is decomposable into a sum of a potent matrix and a nilpotent matrix of order 2. This can be related to our recent paper, published in Linear & Multilinear Algebra (2022). We also completely address the question when each square matrix over an infinite field can be decomposed into a periodic matrix and a nilpotent matrix of order 2\",\"PeriodicalId\":43965,\"journal\":{\"name\":\"Journal of Siberian Federal University-Mathematics & Physics\",\"volume\":\"9 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Siberian Federal University-Mathematics & Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17516/1997-1397-2021-14-5-547-553\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Siberian Federal University-Mathematics & Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17516/1997-1397-2021-14-5-547-553","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
On Some Decompositions of Matrices over Algebraically Closed and Finite Fields
We study when every square matrix over an algebraically closed field or over a finite field is decomposable into a sum of a potent matrix and a nilpotent matrix of order 2. This can be related to our recent paper, published in Linear & Multilinear Algebra (2022). We also completely address the question when each square matrix over an infinite field can be decomposed into a periodic matrix and a nilpotent matrix of order 2
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