{"title":"线性结构","authors":"C. Heunen, J. Vicary","doi":"10.1093/oso/9780198739623.003.0002","DOIUrl":null,"url":null,"abstract":"Many aspects of linear algebra can be reformulated as categorical structures. This chapter examines abstractions of the base field, zero-dimensional spaces, addition of linear operators, direct sums, matrices, inner products and adjoints. These features are essential for modelling features of quantum theory such as superposition, classical data and measurement.","PeriodicalId":314153,"journal":{"name":"Categories for Quantum Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linear Structure\",\"authors\":\"C. Heunen, J. Vicary\",\"doi\":\"10.1093/oso/9780198739623.003.0002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Many aspects of linear algebra can be reformulated as categorical structures. This chapter examines abstractions of the base field, zero-dimensional spaces, addition of linear operators, direct sums, matrices, inner products and adjoints. These features are essential for modelling features of quantum theory such as superposition, classical data and measurement.\",\"PeriodicalId\":314153,\"journal\":{\"name\":\"Categories for Quantum Theory\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-11-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Categories for Quantum Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/oso/9780198739623.003.0002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Categories for Quantum Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/oso/9780198739623.003.0002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Many aspects of linear algebra can be reformulated as categorical structures. This chapter examines abstractions of the base field, zero-dimensional spaces, addition of linear operators, direct sums, matrices, inner products and adjoints. These features are essential for modelling features of quantum theory such as superposition, classical data and measurement.
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