标题:
域上矩阵保乘积的诱导映射Induced Maps Preserving Multiplicative Matrices over Fields
作者:
张隽, 曹重光
关键字:
域, 保乘积, 诱导映射Field, Preserving Multiplicative, Induced Map
期刊名称:
《Pure Mathematics》, Vol.6 No.3, 2016-05-12
摘要:
令F是一个域，Sn(F)是F上所有n*n对称矩阵的集合。如果一个映射f:Sn(F)→Sn(F)被定义如下，∫:B=(bij)|→(fij(bij)), ∀B∈Sn(F)。
其中，{fij|i≤j∈{1,2,...,n}}是关于F的函数集，则称f是Sn(F)的由{fij}诱导的映射。如果对于A,B∈Sn(F)有f(AB)=f(A)f(B)，则f被称为保矩阵乘积。本文我们刻画域上矩阵保乘积的诱导映射。
Let F be a field, Sn(F) be the set of all n*n matrices over F. If a map f:Sn(F)→Sn(F) is defined by ∫:B=(bij)|→(fij(bij))where {fij|i≤j∈{1,2,...,n}} is the set of functions on F, then f is called a map induced by {fij} on Sn(F). If A,B∈Sn(F) implies f(AB)=f(A)f(B), then f is called preserving multiplicative matrices. In this paper, we characterize induced maps preserving multiplicative matrices over fields.