| 主理想整环上对称矩阵的距离与对角化 |
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| 引用本文： | 赵康,黄礼平.主理想整环上对称矩阵的距离与对角化[J].长沙理工大学学报(自然科学版),2006,3(4):81-85. |
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| 作者姓名： | 赵康 黄礼平 |
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| 作者单位： | 长沙理工大学,数学与计算科学学院,湖南,长沙,410076 |
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| 摘 要： | 设R是一个交换主理想整环(PID),A,B是两个R上的对称矩阵,讨论了A与B的算术距离与距离的关系,证明了A-B可合同对角化的充要条件是:A与B的距离等于它们的算术距离.
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| 关 键 词： | 主理想整环(PID) 对称矩阵 算术距离 距离 合同对角化 |
| 文章编号： | 1672-9331（2006）04-0081-05 |
| 收稿时间： | 2006-03-29 |
| 修稿时间： | 2006年3月29日 |
The distance and diagonalization of symmetric matrices over a principal ideal domain |
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| ZHAO Kang,HUANG Li-ping.The distance and diagonalization of symmetric matrices over a principal ideal domain[J].Journal of Changsha University of Science and Technology:Natural Science,2006,3(4):81-85. |
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| Authors: | ZHAO Kang HUANG Li-ping |
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| Institution: | College of Mathmaties and Computing Seienee,Changsha University of Science and Technology, Changsha 410076, China |
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| Abstract: | Let R be a commutative principal ideal domain,A and B be two symmetric matrices over R.We discuss the relationship between the arithmetic distance and the distance of A and B,and prove that A-B is cogradient to a diagonal matrix if and only if the distance between A and B equals to their arithmetic distance. |
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| Keywords: | principal ideal domain(PID) symmetric matrix arithmetic distance distance diagonalization |
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