{"title":"矩阵的克罗内克和分解为不可约矩阵的直接和","authors":"Caixing Gu, Jaehui Park, Chase Peak, J. Rowley","doi":"10.4134/BKMS.B200437","DOIUrl":null,"url":null,"abstract":"In this paper, we decompose (under unitary similarity) the Kronecker sum A A (= A⊗ I + I ⊗A) into a direct sum of irreducible matrices, when A is a 3×3 matrix. As a consequence we identify K(A A) as the direct sum of several full matrix algebras as predicted by Artin– Wedderburn theorem, where K(T ) is the unital algebra generated by T and T ∗.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"58 1","pages":"637-657"},"PeriodicalIF":0.6000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"DECOMPOSITION OF THE KRONECKER SUMS OF MATRICES INTO A DIRECT SUM OF IRREDUCIBLE MATRICES\",\"authors\":\"Caixing Gu, Jaehui Park, Chase Peak, J. Rowley\",\"doi\":\"10.4134/BKMS.B200437\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we decompose (under unitary similarity) the Kronecker sum A A (= A⊗ I + I ⊗A) into a direct sum of irreducible matrices, when A is a 3×3 matrix. As a consequence we identify K(A A) as the direct sum of several full matrix algebras as predicted by Artin– Wedderburn theorem, where K(T ) is the unital algebra generated by T and T ∗.\",\"PeriodicalId\":55301,\"journal\":{\"name\":\"Bulletin of the Korean Mathematical Society\",\"volume\":\"58 1\",\"pages\":\"637-657\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Korean Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4134/BKMS.B200437\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Korean Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/BKMS.B200437","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
DECOMPOSITION OF THE KRONECKER SUMS OF MATRICES INTO A DIRECT SUM OF IRREDUCIBLE MATRICES
In this paper, we decompose (under unitary similarity) the Kronecker sum A A (= A⊗ I + I ⊗A) into a direct sum of irreducible matrices, when A is a 3×3 matrix. As a consequence we identify K(A A) as the direct sum of several full matrix algebras as predicted by Artin– Wedderburn theorem, where K(T ) is the unital algebra generated by T and T ∗.
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This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).
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