三角幂等矩阵上保迹的乘法映射  

Multiplicative Maps on Triangular Idempotent Matrices that Preserve the Trace

作　　者：黄弘[1] 胡付高[1] 

机构地区：[1]孝感学院数学系,湖北孝感432000

出　　处：《孝感学院学报》2007年第6期32-33,共2页JOURNAL OF XIAOGAN UNIVERSITY

摘　　要：An(F)({aEij︱1≤i≤j≤n})为域F上n阶上三角矩阵Tn(F)上的幂等矩阵集nГ(F)的乘法半群。f:An(F)→Гn(F)是满足trf(A)=trA,A∈An(F)的乘法映射,那么存在可逆上三角矩阵P∈Tn(F),使得f(A)=P-1AP。An(F)({aEij︱1≤i≤j≤n}) is a multiplicative semigoup on field F,which An(F) belongs to n×n upper triangular idempotent matrix set Гn(F) over F.Let f:An(F)→Гn(F) is a multiplicative map which satisfies trf(A)=trA,A∈An(F),then there exists an invertible upper triangular matrix P∈Tn(F),such that f(A)=P-1AP.

关 键 词：三角幂等矩阵 保迹 乘法映射 

分 类 号：O151.21[理学—数学]