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 数学进展
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 四元数矩阵的酉相合与酉相似(英文) Unitary Congruence and Unitary Similarity for Quaternion Matrix 蔡永裕;黄礼平; CAI Yongyu~ 湖南科技大学数学与计算科学学院;长沙理工大学数学与计算科学学院; (1,*),HUANG Liping~2 (1.School of Mathematics and Computing Science,Hunan University of Science and Technology, Xiangtan,Hunan,411201,P.R.China;2.School of Mathematics and Computing Science,Changsha University of Science and Technology,Changsha,Hunan,4100 收稿日期: 2009-06-25 出版日期: 2009-06-25
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 摘要 本文讨论了四元数矩阵的酉相合,四元数矩阵的酉相合是复矩阵的复酉相合的自然推广,并且它有许多好的性质.由于四元数矩阵的酉相合与酉相似有着密切联系,本文还讨论了四元数矩阵的酉相似的一些性质. 关键词 ： 四元数矩阵,  酉相合,  复酉相合,  合相似,  酉相似 Abstract：This paper discusses the unitary congruence of quaternion matrices,the unitary congruence of quaternion matrices is natural extension of the complex unitary congruence of complex matrices and has many good properties.Since unitary congruence of quaternion matrices is in connection with unitary similarity of quaternion matrices,we also discuss some properties of the unitary similarity of quaternion matrices. Key words： unitary congruence    complex unitary congruence    consimilar    unitary similarity
 [1] 庄瓦金. 四元数矩阵的极分解及其GL偏序[J]. 数学进展, 2005, 34(2): 187-193. [2] 黄礼平. 四元数自共轭矩阵乘积的相似变换[J]. 数学进展, 2003, 32(4): 429-434.
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