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| 可换对称矩阵上的非线性k次幂等保持映射(英文) | |
| 引用本文： | 韩秀,偶世坤,夏春光.可换对称矩阵上的非线性k次幂等保持映射(英文)[J].安徽大学学报(自然科学版),2011,35(6):15-19. |
| 作者姓名： | 韩秀 偶世坤 夏春光 |
| 作者单位： | 1. 徐州工程学院数学与物理科学学院,江苏徐州,221008 2. 江西理工大学理学院,江西赣州,341000 3. 中国科学技术大学吴文俊数学重点实验室,安徽合肥,230026 |
| 基金项目： | Supported by the Youth Foundation of Jiangxi Provincial Education Department of China(GJJ10155) |
| 摘 要： | 线性保持问题主要研究矩阵空间上保持某种函子、子集合或者某种关系式等不变的算子.研究了复数域上对称矩阵空间的非线性保持问题,运用矩阵计算技巧和数学归纳法,证明了可换对称矩阵组A=(A1,A2,…,Ad)上保持k次幂等的非线性映射是一个k次单位根与一个依赖于A的内自同构的乘积.这一结论是一些已知结果的重要补充. |
| 关 键 词： | 非线性保持 k次幂等矩阵 可换矩阵组 |
Non-linear k-potence preserving maps on commuting symmetric matrices |
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| HAN Xiu,OU Shi-kun,XIA Chun-guang.Non-linear k-potence preserving maps on commuting symmetric matrices[J].Journal of Anhui University(Natural Sciences),2011,35(6):15-19. | |
| Authors: | HAN Xiu OU Shi-kun XIA Chun-guang |
| Institution: | HAN Xiu1,OU Shi-kun2,XIA Chun-guang3(1.School of Mathematics and Physical Science,Xuzhou Institute of Technology,Xuzhou 221008,China,2.School of Science,Jiangxi University of Science and Technology,Ganzhou 341000,3.Wu Wen-Tsun Key Laboratory of Mathematics,University of Science and Technology of China,Hefei 230026,China) |
| Abstract: | Linear preserver problems mainly investigate the operators on matrix spaces that leave certain functions,subsets,relations,etc.,invariant.Nonlinear preserver problem on symmetric matrices over complex field is investigated in the present paper.By using matrix computational techniques and induction,it is shown that the nonlinear maps on commuting symmetric matricesA =(A1,A2,…,Ad) that preserve k-potent is a product of a k-th root of unity and an inner automorphism depending on A.The conclusion is an important supplement of some known results. |
| Keywords: | non-linear preserver k-potent matrix commuting matrix |
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