| 域上保上三角矩阵逆的线性映射 |
| |
| 引用本文： | 曹重光,吴海燕. 域上保上三角矩阵逆的线性映射[J]. 高师理科学刊, 2006, 26(1): 4-6 |
| |
| 作者姓名： | 曹重光 吴海燕 |
| |
| 作者单位： | 黑龙江大学,数学科学学院,黑龙江,哈尔滨,150080 |
| |
| 摘 要： | 设F是一个元素个数大于3的域,n 2是一个正整数,令Mn(F)和Tn(F)分别是F上n×n全矩阵空间和上三角矩阵空间,首先刻画从Tn(F)到Mn(F)的保矩阵逆的所有线性单射,由此Tn(F)到自身的所有保矩阵逆的线性双射被刻画.
|
| 关 键 词： | 域 保逆线性映射 全矩阵空间 上三角矩阵空间 |
| 文章编号： | 1007-9831(2006)01-0004-03 |
| 修稿时间： | 2005-09-02 |
Linear maps preserving inverses of upper triangular matrices over fields |
| |
| CAO Chong-guang,WU Hai-yan. Linear maps preserving inverses of upper triangular matrices over fields[J]. Journal of Science of Teachers＇College and University, 2006, 26(1): 4-6 |
| |
| Authors: | CAO Chong-guang WU Hai-yan |
| |
| Abstract: | Suppose F is a field with the number of elements larger than 3,n2 is a positive integer.Let(M_n(F)) and T_n(F) be the linear spaces of n×n full matrices and upper triangular matrices over F,respectively.The paper first characterizes all linear injective maps from T_n(F) to M_n(F) preserving inverses of matrices,and thereby all linear bijective maps from T_n(F) to itself preserving inverses of matrices are characterized. |
| |
| Keywords: | fields linear map preserving inverse space of full matrices space of upper triangular matrices |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
