| 交错矩阵空间之间保持伴随矩阵的线性映射 |
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| 引用本文： | 张杨.交错矩阵空间之间保持伴随矩阵的线性映射[J].哈尔滨工业大学学报,2008,40(2):279-281. |
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| 作者姓名： | 张杨 |
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| 作者单位： | 哈尔滨工业大学,数学系,哈尔滨,150001 |
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| 摘 要： | 设n,m为两个大于或等于4的偶数,F是任意域且F≠{0,1}.用Kn(F)和Km(F)分别表示域F上所有n×n和m×m交错矩阵所组成的空间.刻画了从Kn(F)到Km(F)的保持伴随矩阵的线性映射,证明了刻画不同维的交错矩阵空间之间保持伴随矩阵的线性映射的形式最终可归结为刻画同维的交错矩阵空间之间保持秩2和秩4矩阵的线性映射的形式,丰富了矩阵空间上保持问题的成果.
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| 关 键 词： | 交错矩阵 伴随矩阵 线性映射 保持 |
| 文章编号： | 0367-6234(2008)02-0279-03 |
| 修稿时间： | 2005年12月22 |
Linear maps preserving adjoint matrix between alternate matrix spaces |
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| ZHANG Yang.Linear maps preserving adjoint matrix between alternate matrix spaces[J].Journal of Harbin Institute of Technology,2008,40(2):279-281. |
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| Authors: | ZHANG Yang |
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| Affiliation: | ZHANG Yang(Dept.of Mathematics,Harbin Institute of Technology,Harbin 150001,China,) |
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| Abstract: | Suppose n,m≥4 are even and F is any field except for {0,1}.Let Kn(F) and(Km(F) respectively be the space of all n×n and m×m) alternate matrices over F.The linear maps from Kn(F) to Km(F) that preserve adjoint matrix are characterized.Then it can be concluded that,the form of linear maps preserving adjoint matrix between different dimensional spaces of alternate matrices can be reduced to characterize the form of linear maps preserving rank 2 and 4 the alternate matrices among in the same dimensional space.This enriches the results of preserver problems on spaces of matrices. |
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| Keywords: | alternate matrix adjoint matrix linear map preserve |
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