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.
出处
《孝感学院学报》
2007年第6期32-33,共2页
JOURNAL OF XIAOGAN UNIVERSITY
关键词
三角幂等矩阵
保迹
乘法映射
triangular idempotent matrix
trace-preserving
multiplicative map
