对称及反对称矩阵空间的保持逆矩阵的函数  

Function preserving inverses of symmetric and anti-symmetric matrices

作　　者：樊玉环[1] 袁海燕[1] 魏喆[1] FAN Yu-huan;YUAN Hai-yan;WEI Zhe(College of Science,Heilongjiang Institute of Technology,Harbin 150010)

机构地区：[1]黑龙江工程学院理学院,哈尔滨150010

出　　处：《哈尔滨商业大学学报（自然科学版）》2021年第3期356-362,共7页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：黑龙江省自然科学基金(LH2019A030)。

摘　　要：针对函数保持的问题,依据线性代数及近世代数中的相关理论,采用证明推理的方法,在对称矩阵空间或者反对称矩阵空间里找到两个互逆的矩阵,经函数作用后,得到两个新的矩阵仍然是互逆的关系,对此函数的具体形式进行刻画,得到对称矩阵空间或者是反对称矩阵空间上的保持逆矩阵的函数实际上是域上的一个满足某一条件的单自同态.For the problem of function preservation,according to the theory of linear algebra and modern algebra,the method of proof and inference was used,and the special reciprocal matrices of symmetric and anti-symmetric matrices were found.After the function action,the two new matrices were still reciprocal.The concrete form of function was depicted.At last,the conclusion that the function was actually a simple endomorphism satisfying the condition was obtained.

关 键 词：保持 函数 对称矩阵空间 反对称矩阵空间 逆矩阵 

分 类 号：O153.3[理学—数学]