| 域上两类矩阵保逆的诱导映射 |
| |
| 引用本文： | 闫盼盼,曹重光. 域上两类矩阵保逆的诱导映射[J]. 纯粹数学与应用数学, 2016, 32(2): 149-159. DOI: 10.3969/j.issn.1008-5513.2016.02.006 |
| |
| 作者姓名： | 闫盼盼 曹重光 |
| |
| 作者单位： | 黑龙江大学数学科学学院,黑龙江 哈尔滨,150080;黑龙江大学数学科学学院,黑龙江 哈尔滨,150080 |
| |
| 基金项目： | 国家自然科学基金(11371109) |
| |
| 摘 要： | 令F是一个域,S_n(F)是F上所有n×n上对称矩阵的集合.用T_n(F)记F上所有n阶上三角阵的集合.首先分别给出诱导映射和保逆性的定义.然后改进了关于复对称阵保逆的主要相关结果及其证明,得到了S_n(F)保逆诱导映射的一般形式,最后借助于类序列技术和初等方法刻画了T_n(F)保逆诱导映射.它推广和改进了带有附加条件(f_(ij)(x)=0x=0)的相关结果.
|
| 关 键 词： | 域 对称矩阵 上三角矩阵 保逆 诱导映射 |
Induced maps preserving inveres of two kinds of matrices over fields |
| |
| Yan Panpan,Cao Chongguang. Induced maps preserving inveres of two kinds of matrices over fields[J]. Pure and Applied Mathematics, 2016, 32(2): 149-159. DOI: 10.3969/j.issn.1008-5513.2016.02.006 |
| |
| Authors: | Yan Panpan Cao Chongguang |
| |
| Abstract: | Supposed that F is a field and n ≥3 is an integer.Denote bySn(F) the set of all n × n symmetric matrices over F , Tn(F) the set of all n × n upper triangular matrices over F . First, the paper gives the definition of induced map and preserving inveres, respectively. And then, proof of main result about preserving inveres on symmetric matrices is improved,the general forms of induced maps preserving inverses on Sn(F) is obtained.Finally,induced maps preserving inveres on Tn(F) is characterized by class-sequence technigues and elementary methods,which generalize and improve relevant results with strings attached(fij (x)=0?x=0). |
| |
| Keywords: | field symmetric matrix upper triangular matrix preserving inveres induced map |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
