{"title":"具有子矩阵约束的矩阵方程(AX = B, XC = D)的解","authors":"Fan-Liang Li, Xiyan Hu, Lei Zhang","doi":"10.1109/ICNC.2008.535","DOIUrl":null,"url":null,"abstract":"In this paper, the solvability conditions and the general solution of matrix equations (AX=B,XC=D) with a submatrix constraint are obtained by using the SVD(singular value decomposition) of matrix. In addition, the expression of the optimal approximation solution to a given matrix is derived.","PeriodicalId":6404,"journal":{"name":"2008 Fourth International Conference on Natural Computation","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2008-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Solutions of Matrix Equations (AX = B, XC = D) with a Submatrix Constraint\",\"authors\":\"Fan-Liang Li, Xiyan Hu, Lei Zhang\",\"doi\":\"10.1109/ICNC.2008.535\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the solvability conditions and the general solution of matrix equations (AX=B,XC=D) with a submatrix constraint are obtained by using the SVD(singular value decomposition) of matrix. In addition, the expression of the optimal approximation solution to a given matrix is derived.\",\"PeriodicalId\":6404,\"journal\":{\"name\":\"2008 Fourth International Conference on Natural Computation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-10-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2008 Fourth International Conference on Natural Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICNC.2008.535\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2008 Fourth International Conference on Natural Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICNC.2008.535","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Solutions of Matrix Equations (AX = B, XC = D) with a Submatrix Constraint
In this paper, the solvability conditions and the general solution of matrix equations (AX=B,XC=D) with a submatrix constraint are obtained by using the SVD(singular value decomposition) of matrix. In addition, the expression of the optimal approximation solution to a given matrix is derived.
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