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 M_n(F) and S_n(F)be the n×n full matrix algebra and symmetric matrix algebra over F, respectively. All linear maps from S_n (F) to M_n (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 S_n (F) to M_n (F) preserving group inverses of matrices.
出处
《数学杂志》
CSCD
北大核心
2005年第2期130-134,共5页
Journal of Mathematics
基金
Supported by Natural Science Foundation of Heilongjiang Province (A01 07)
the NSF of Heilongjiang Education Committee (15011014).
关键词
域
特征数
矩阵的群逆
线性映射
全矩阵代数
对称矩阵代数
相似标准形
field
characteristic
group inverse of matrix
linear map
full matrix algebra
symmetric matrix algebra
similar canonical form
