域上2阶全矩阵空间保次交换的线性映射

Commutativity degree-preserving linear maps on 2×2 matrix spaces over any field

在保持问题的研究中,2?2阶矩阵空间的研究方法具有一定的特殊性.设F是域,2M(F)记为F上2阶全矩阵空间,刻画了2M(F)上保次交换的线性映射的形式.

The research of preserver problems over 2？2 matrix spaces has its speciality.Suppose F is any field,let M 2 （F ） denote 2？2 matrix spaces over F .Characterized the form of commutativity degree-preserving linear maps over M 2 （F ） .