Hermite矩阵保秩1导出映射

Produced Maps Preserving Rank One on Hermitian Matrices

设C是复数域,fij(i,j∈[n]■{1,2,…,n})是从C到自身的映射,Hn(C)是C上n阶Hermite矩阵全体所成集合,f是Hn(C)上由{fij}n诱导的映射,在f(0)=0条件下给出了Hn(C)上保秩1的导出映射的形式。

Let C be the field of complex numbers, and let fij（i,j∈[n]△{1,3,…,n}）be the map form Cinto itself. Denote by Hn（C） the set of all Hermitain matrices of order n over C. Let f be the produced map by {fij}non Hn（C）. In this paper, we describe the forms of all produced maps preserving rank one on Hn（C）in the case f（0）/=0.