{"title":"一类算子矩阵的特征向量展开式定理","authors":"Y. Qiao","doi":"10.7498/aps.61.140205","DOIUrl":null,"url":null,"abstract":"An expansion theorem of a class of operator matrices is set up.The symplectic orthogonality of eigen-vectors is obtaind,and a necessary and sufficient condition for the completeness of the eigen-vector system is further given.As concrete applications,the obtained results are tested for differential equations.","PeriodicalId":16190,"journal":{"name":"Journal of Inner Mongolia University","volume":"58 2-3","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Eigen-vector Expansion Theorem of a Class of Operator Matrices\",\"authors\":\"Y. Qiao\",\"doi\":\"10.7498/aps.61.140205\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An expansion theorem of a class of operator matrices is set up.The symplectic orthogonality of eigen-vectors is obtaind,and a necessary and sufficient condition for the completeness of the eigen-vector system is further given.As concrete applications,the obtained results are tested for differential equations.\",\"PeriodicalId\":16190,\"journal\":{\"name\":\"Journal of Inner Mongolia University\",\"volume\":\"58 2-3\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Inner Mongolia University\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7498/aps.61.140205\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Inner Mongolia University","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7498/aps.61.140205","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Eigen-vector Expansion Theorem of a Class of Operator Matrices
An expansion theorem of a class of operator matrices is set up.The symplectic orthogonality of eigen-vectors is obtaind,and a necessary and sufficient condition for the completeness of the eigen-vector system is further given.As concrete applications,the obtained results are tested for differential equations.
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