Pub Date : 2020-07-09DOI: 10.1017/9781108151689.009
Матрицы И Системы, Линейных Уравнений, V. A. Brusin
Если изначально имеется только одно или два уравнения, то недостающие уравнения можно приписать, повторив уже имеющиеся. Аналогично если имеются три уравнения, но только два неизвестных x 1 и x 2 , то можно дополнить эти уравнения членами с неизвестным x 3 и нулевыми коэффициентами a i 3 , приведя систему к виду (1). Как известно [2, 3], решением системы (1) называется тройка чисел ( x 1 , x 2 , x 3 ), которая после подстановки в систему (1) обращает каждое уравнение в тождество. Известно также, что система (1) может иметь единственное решение, бесчисленное множество решений или не иметь решений вообще. Ниже, используя матричный аппарат и интерпретацию матриц как операторов [1], мы дадим геометрическую трактовку этим трем случаям. Введем в рассмотрение квадратную матрицу A , столбцы b и x :
如果最初只有一个或两个方程，那么丢失的方程可以通过重复现有的方程来分配。如果有三个方程类似,但只有两个未知数x 1 x 2,可以补充这些方程和未知成员i 3 x 3和零系数a,把系统(1)。众所周知[2,3],解决系统(1)称为实数c (x, x 2 x 3)置换后的系统(1)每个方程变成恒等式。众所周知，系统(1)可以有一个解决方案，无数的解决方案，也可以根本没有解决方案。下面，使用矩阵设备和矩阵解释为运算符，我们将对这三种情况进行几何解释。让我们考虑一个二次矩阵A, b列和x:
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Pub Date : 2020-07-09DOI: 10.1017/9781108151689.004
{"title":"Modeling Aspects","authors":"","doi":"10.1017/9781108151689.004","DOIUrl":"https://doi.org/10.1017/9781108151689.004","url":null,"abstract":"","PeriodicalId":313531,"journal":{"name":"Finite Elements for Engineers with ANSYS Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133013016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-09DOI: 10.1017/9781108151689.003
{"title":"Detailed Procedures","authors":"","doi":"10.1017/9781108151689.003","DOIUrl":"https://doi.org/10.1017/9781108151689.003","url":null,"abstract":"","PeriodicalId":313531,"journal":{"name":"Finite Elements for Engineers with ANSYS Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128553543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-09DOI: 10.1016/b978-0-12-818994-8.00019-1
K. Wichterle, M. Večeř
{"title":"Vectors and Tensors","authors":"K. Wichterle, M. Večeř","doi":"10.1016/b978-0-12-818994-8.00019-1","DOIUrl":"https://doi.org/10.1016/b978-0-12-818994-8.00019-1","url":null,"abstract":"","PeriodicalId":313531,"journal":{"name":"Finite Elements for Engineers with ANSYS Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128473745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-09DOI: 10.1017/9781108151689.012
{"title":"Index","authors":"","doi":"10.1017/9781108151689.012","DOIUrl":"https://doi.org/10.1017/9781108151689.012","url":null,"abstract":"","PeriodicalId":313531,"journal":{"name":"Finite Elements for Engineers with ANSYS Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132413761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-09DOI: 10.1017/9781108151689.005
{"title":"Linear Static Analysis Using Ansys/Workbench","authors":"","doi":"10.1017/9781108151689.005","DOIUrl":"https://doi.org/10.1017/9781108151689.005","url":null,"abstract":"","PeriodicalId":313531,"journal":{"name":"Finite Elements for Engineers with ANSYS Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130789315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-30DOI: 10.1017/9781108149914.002
E. Silk
{"title":"Conduction Heat Transfer Analysis","authors":"E. Silk","doi":"10.1017/9781108149914.002","DOIUrl":"https://doi.org/10.1017/9781108149914.002","url":null,"abstract":"","PeriodicalId":313531,"journal":{"name":"Finite Elements for Engineers with ANSYS Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116778923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Finite Element Concepts","authors":"E. Dill","doi":"10.1201/b11455-4","DOIUrl":"https://doi.org/10.1201/b11455-4","url":null,"abstract":"","PeriodicalId":313531,"journal":{"name":"Finite Elements for Engineers with ANSYS Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132354854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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