{"title":"Vectors on manifolds","authors":"A. Steane","doi":"10.1093/oso/9780192895646.003.0009","DOIUrl":null,"url":null,"abstract":"The vector, the dual vector (one-form), components and inner products are defined and discussed. The difference between a vector and a one-form is carefully drawn out, with examples and diagrams. Contravariant and covariant components are described, and the way in which the metric can relate them is carefully explained. The transformation of vector components under a change of coordinate basis is derived.","PeriodicalId":365636,"journal":{"name":"Relativity Made Relatively Easy Volume 2","volume":"31 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Relativity Made Relatively Easy Volume 2","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/oso/9780192895646.003.0009","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The vector, the dual vector (one-form), components and inner products are defined and discussed. The difference between a vector and a one-form is carefully drawn out, with examples and diagrams. Contravariant and covariant components are described, and the way in which the metric can relate them is carefully explained. The transformation of vector components under a change of coordinate basis is derived.
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