{"title":"Uniqueness of the Tensor Decomposition for Tensors With Small Ranks Over a Field","authors":"E. Ballico","doi":"10.47443/ejm.2022.007","DOIUrl":null,"url":null,"abstract":"We study the uniqueness of a decomposition of a tensor over a field as a sum of rank 1 tensors, when the tensor has low rank, up to 3 . We put this in a more general framework ( X -rank) and study two different definitions of decompositions over a given (not algebraically closed) field","PeriodicalId":29770,"journal":{"name":"International Electronic Journal of Mathematics Education","volume":"20 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Electronic Journal of Mathematics Education","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.47443/ejm.2022.007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"EDUCATION & EDUCATIONAL RESEARCH","Score":null,"Total":0}
引用次数: 0
Abstract
We study the uniqueness of a decomposition of a tensor over a field as a sum of rank 1 tensors, when the tensor has low rank, up to 3 . We put this in a more general framework ( X -rank) and study two different definitions of decompositions over a given (not algebraically closed) field
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