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Huang, L.P. (2006) Geometry of Matrices over Ring. Science Press.

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  • 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: , 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.