矩阵空间上线性保持问题的几个结果(英文)

Several results on linear preserver problems on spaces of matrices

设Mn(F)表示域F上所有n×n矩阵构成的线性空间,sln(F)表示Mn(F)的包含所有迹零矩阵的子空间。基于一些现有的结论,刻划了Mn(F)上可逆的线性秩1平方零(平方零、对合)保持,以及Mn(F)上强线性平方零(对合)保持,所获得的结果展示了几类线性保持问题间的关系。

Let Mn（F）be the linear space of all n×n matrices over a field F,and let sln（F）be the subspace of Mn（F）consisting of all zero-trace matrices.Based on some existing results,all invertible linear rank-1 square-zero（respectively,square-zero,involution）preservers on Mn（F）are characterized,and the structures of all strong linear square-zero（respectively,involution）preservers on Mn（F）are described.These results obtained here show clearly the relations among several linear preserver problems.