摘要
令F是一个域,T_n(F)是F上所有n×n上三角矩阵的集合.本文分别给出了矩阵保相似性及保交换性的定义,并使用矩阵技术和初等方法,得到了T_n(F)的保相似性及保交换性的诱导映射的一般形式,并且给出了例子,来解释一些结果之间的关系.
Let F is a field and Tn(F) is a set of all n n upper triangular matrices over F. In this paper thede nition of preserving similarity and commutativity about matvix are given respectively. This paper gets thegeneral forms of induced maps about preserving similarity and commutativity by using the techniques of matrixand elementary method and explain the relationship between the results through examples.
作者
付丽
闫盼盼
曹重光
Fu Li;Yan Panpan;Cao Chongguang(School of Information Engineering, Suihua University, Suihua 152061, China;School of Mathematical Science, Heilongjiang University, Harbin 150080, China)
出处
《纯粹数学与应用数学》
2016年第6期630-639,共10页
Pure and Applied Mathematics
基金
国家自然科学基金(11371109)
绥化学院2015年科学技术研究项目(K1502004)
关键词
上三角矩阵
保相似性
保交换性
诱导映射
upper triangular tatrix
preserving similarity
preserving commutativity
induced map
