保特征2域上上三角矩阵群逆的线性映射

Linear Maps Preserving Group Inverses of Triangular Matrices Over a Field of Characteristic 2

设F是一个特征2且至少含有5个元素的域,n 2是一个正整数.令Mn(F)和Tn(F)分别F上的全矩阵空间和上三角矩阵空间.我们首先刻划从Tn(F)到Mn(F)的保矩阵群逆的所有线性单射.由此从Tn(F)到自身的所有保矩阵群逆的线性双射被刻划.

Suppose F is a field of characteristic 2 with at least five elements, and n≥2 is a positive integer. Let Mn（F） and Tn （F） be the linear spaces of n×n full matrices and upper triangular matrices over F, respectively. We first characterize all linear injective maps from Tn（F） to Mn（F） preserving group inverses of matrices, and thereby all linear bejective maps from Tn（F） to itself preserving group inverses of matrices are characterized.