域上两类矩阵保逆的诱导映射

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(fij (x)=0⇔x=0)的相关结果。%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).