{"title":"块Toeplitz矩阵:乘法性质","authors":"M. A. Khan","doi":"10.11113/matematika.v39.n1.1437","DOIUrl":null,"url":null,"abstract":"Given A, B, C, and D, block Toeplitz matrices, we will prove the necessary and sufficient condition for AB - CD = 0, and AB - CD to be a block Toeplitz matrix. In addition, with respect to change of basis, the characterization of normal block Toeplitz matrices with entries from the algebra of diagonal matrices is also obtained.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":"1 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2021-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Block Toeplitz Matrices: Multiplicative Properties\",\"authors\":\"M. A. Khan\",\"doi\":\"10.11113/matematika.v39.n1.1437\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given A, B, C, and D, block Toeplitz matrices, we will prove the necessary and sufficient condition for AB - CD = 0, and AB - CD to be a block Toeplitz matrix. In addition, with respect to change of basis, the characterization of normal block Toeplitz matrices with entries from the algebra of diagonal matrices is also obtained.\",\"PeriodicalId\":43733,\"journal\":{\"name\":\"Matematika\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-03-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11113/matematika.v39.n1.1437\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11113/matematika.v39.n1.1437","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Given A, B, C, and D, block Toeplitz matrices, we will prove the necessary and sufficient condition for AB - CD = 0, and AB - CD to be a block Toeplitz matrix. In addition, with respect to change of basis, the characterization of normal block Toeplitz matrices with entries from the algebra of diagonal matrices is also obtained.
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