从对称矩阵代数到全矩阵代数的线性群逆保持

摘要

设F是一个特征不为2的域,Mn(F)和Sn(F)分别记F上的n×n全矩阵代数和对称矩阵代数.所有的从Sn(F)到Mn(F)的保群逆的线性映射被刻划,作为一个中间步骤,三个矩阵的同时相似标准形也被证明.这个标准形简化了从Sn(F)到Mn(F)的保群逆的线性映射的刻划.%Suppose F is a field of characteristic not 2.Let Mn(F) and Sn(F)be the n×n full matrix algebra and symmetric matrix algebra over F, respectively. All linear maps from Sn (F) to Mn (F) preserving group inverses of matrices are characterized. As a medium step, a similar canonical form of a matrix triple is also obtained. The similar canonical form simplifies the process of characterizing linear maps from Sn (F) to Mn (F) preserving group inverses of matrices.