{"title":"Study of diagonalization on skew self-conjugate matrix in quaternion field","authors":"Lieya Yan, L. Xu","doi":"10.1109/CINC.2010.5643889","DOIUrl":null,"url":null,"abstract":"This paper made a further research based on the extended unitary diagonalization of skew self-conjugate matrix. Based on the definition of skew selfconjugate matrix, we discussed some properties of skew self-conjugate matrix, and gave the necessary and sufficient condition for determining whether ; is a right eigenvalue of matrix in the quaternion field. By means of the Schur theorem in real quaternion field, we proved that skew self-conjugate can be extended unitary diagonalized. Furthermore, if A and B are invertible and commutative, then A + B and A−1 + B−1 can be extended unitary diagonalized at the same time.","PeriodicalId":227004,"journal":{"name":"2010 Second International Conference on Computational Intelligence and Natural Computing","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 Second International Conference on Computational Intelligence and Natural Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CINC.2010.5643889","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
This paper made a further research based on the extended unitary diagonalization of skew self-conjugate matrix. Based on the definition of skew selfconjugate matrix, we discussed some properties of skew self-conjugate matrix, and gave the necessary and sufficient condition for determining whether ; is a right eigenvalue of matrix in the quaternion field. By means of the Schur theorem in real quaternion field, we proved that skew self-conjugate can be extended unitary diagonalized. Furthermore, if A and B are invertible and commutative, then A + B and A−1 + B−1 can be extended unitary diagonalized at the same time.