| 矩阵几何在保持问题中的几个应用 |
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| 引用本文： | 曹重光,唐孝敏,黄礼平.矩阵几何在保持问题中的几个应用[J].数学研究及应用,2007,27(4):697-703. |
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| 作者姓名： | 曹重光 唐孝敏 黄礼平 |
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| 作者单位： | 1. 黑龙江大学数学系,黑龙江,哈尔滨,150080
2. 长沙理工大学数学与计算科学学院,湖南,长沙,410076 |
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| 基金项目： | 国家自然科学基金;黑龙江省教育厅科学技术研究项目 |
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| 摘 要： | 借助矩阵几何基本定理,关于矩阵空间的某些半线性保持算子和加法保持算子被刻画.例如,秩可加性保持,全矩阵环的弱半自同构,幂等性保持,平方保持,以及交错阵的粘切性保持.
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| 关 键 词： | 矩阵几何 线性保持问题 半线性算子 交错矩阵. |
| 文章编号： | 1000-341X（2007）04-0697-07 |
| 收稿时间： | 2005/12/5 0:00:00 |
| 修稿时间： | 2005-12-05 |
Several Applications of Geometry of Matrices in Preserver Problem |
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| CAO Chong-guang,TANG Xiao-min and HUANG Li-ping.Several Applications of Geometry of Matrices in Preserver Problem[J].Journal of Mathematical Research with Applications,2007,27(4):697-703. |
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| Authors: | CAO Chong-guang TANG Xiao-min and HUANG Li-ping |
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| Institution: | Department of Mathematics, Heilongjiang University, Heilongjiang 150080, China;Department of Mathematics, Heilongjiang University, Heilongjiang 150080, China;School of Mathematics and Computing Science, Changsha University of Science and Technology, Hunan 410076, China |
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| Abstract: | By the fundamental theorems of the geometry of matrices,some semi-linear preserver op- erators and additive preserver operators on matrix spaces are characteriged,including rank-additivety preservers,weak semi-automorphisms of the full matrix ring,idempotence preservers,2-potent matrices preservers,and the adjacency preservers of altenate matrices. |
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| Keywords: | geometry of matrices linear preserver problems semilinear operator alternate matrix |
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