| 关于广义四元数代数上矩阵的迹的一个等式 |
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| 引用本文： | 程士珍,田永革.关于广义四元数代数上矩阵的迹的一个等式[J].数学研究及应用,2006,26(1):43-46. |
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| 作者姓名： | 程士珍 田永革 |
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| 作者单位： | 1. 北京建筑工程学院基础部,北京,100044;北京师范大学数学科学学院,北京,100875
2. 加拿大皇后大学数学与统计系,K7L3N6 |
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| 摘 要： | 众所周知,相似矩阵的迹相等对于非交换代数和环上的矩阵不一定成立,有趣的问题是给定一个条件使得相似矩阵的迹相等对于非交换代数或非交换环上的矩阵成立。本文对于特征不是2的任意域F上定义的广义四元数代数上的两个矩阵A和B,给出如果A和B相似并且它们的主对角线上的元素在F中,那么它们的迹相等。
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| 关 键 词： | 广义四元数代数 矩阵 相似 迹 |
| 文章编号： | 1000-341X(2006)01-0043-04 |
| 收稿时间： | 10 8 2003 12:00AM |
| 修稿时间： | 2003年10月8日 |
An Equality for Trace of Matrix over a Generalized Quaternion Algebra |
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| CHENG Shi-zhen and TIAN Yong-ge.An Equality for Trace of Matrix over a Generalized Quaternion Algebra[J].Journal of Mathematical Research with Applications,2006,26(1):43-46. |
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| Authors: | CHENG Shi-zhen and TIAN Yong-ge |
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| Institution: | Dept. of Basic Sci.; Beijing Institute of Civil Engineering and Architecture; Beijing; China; School of Mathematical Sciences; Beijing Normal University; Beijing; China;Dept. of Math. and Statistics; Queen's University Kingston; Ontario; Canada K7L 3N6 |
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| Abstract: | The well-known trace equality of similar matrices does not necessarily hold for matrices over non-commutative algebras and rings. An interesting question is to give conditions such that trace equality of similar matrices holds for matrices over a non-commutative algebra or ring. In this note, we show that for any two matrices A and B over a generalized quaternion algebra denned on an arbitrary field F of characteristic not equal to two, if A and B are similar and the main diagonal elements of A and B are in F, then their traces are equal. |
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| Keywords: | generalized quaternion algebra matrix similarity trace |
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