{"title":"基于改进qr算法的矩阵的Kronecker积及其在线性系统中的应用","authors":"N. V. Lakshmi, Jajula Madhu, Musa Dileep Durani","doi":"10.18535/ijecs/v10i6.4600","DOIUrl":null,"url":null,"abstract":"This paper studies and supplements the proofs of the properties of the Kronecker Product of two matrices of different orders. We observe the relation between the singular value decomposition of the matrices and their Kronecker product and the relationship between the determinant, the trace, the rank and the polynomial matrix of the Kronecker products. We also establish the best least square solutions of the Kronecker product system of equations by using modified QR-algorithm.","PeriodicalId":231371,"journal":{"name":"International Journal of Engineering and Computer Science","volume":"56 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the Kronecker Product of Matrices and Their Applications To Linear Systems Via Modified QR-Algorithm\",\"authors\":\"N. V. Lakshmi, Jajula Madhu, Musa Dileep Durani\",\"doi\":\"10.18535/ijecs/v10i6.4600\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper studies and supplements the proofs of the properties of the Kronecker Product of two matrices of different orders. We observe the relation between the singular value decomposition of the matrices and their Kronecker product and the relationship between the determinant, the trace, the rank and the polynomial matrix of the Kronecker products. We also establish the best least square solutions of the Kronecker product system of equations by using modified QR-algorithm.\",\"PeriodicalId\":231371,\"journal\":{\"name\":\"International Journal of Engineering and Computer Science\",\"volume\":\"56 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-06-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Engineering and Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18535/ijecs/v10i6.4600\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Engineering and Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18535/ijecs/v10i6.4600","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Kronecker Product of Matrices and Their Applications To Linear Systems Via Modified QR-Algorithm
This paper studies and supplements the proofs of the properties of the Kronecker Product of two matrices of different orders. We observe the relation between the singular value decomposition of the matrices and their Kronecker product and the relationship between the determinant, the trace, the rank and the polynomial matrix of the Kronecker products. We also establish the best least square solutions of the Kronecker product system of equations by using modified QR-algorithm.
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