关于域上矩阵广义逆的加法映射  

Additive Maps on Generalized Inverses of Matrices over Fields

作　　者：张显[1] 曹重光[1] 

机构地区：[1]黑龙江大学数学系,哈尔滨150080

出　　处：《数学学报（中文版）》2004年第5期1013-1018,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10271021);黑龙江省自然科学基金资助项目(A01-07)

摘　　要：假设F是特征不为2的域,令Mn(F)是F上n×n矩阵的集合.本文证明了f是Mn(F)到自身的矩阵{1}-逆或{1,2}-逆的加法保持算子当且仅当f有:(a)f=0;(b)f(A)=εPAτP-1对任意A∈Mn(F),其中P∈GLn(F),τ-为域F的某个单自同态且x(1)=1,ε=±1;(c)f(A)=εP(Aτ)TP-1对于任意A∈Mn(F),其中τ,ε,P如(b)中一样意义.Suppose F is a field of characteristic other than 2. Let Mn(F) be the set of n × n matrices over F. We show that f : Mn(F) → Mn(F) is an additive preserver of {1}-inverses or {1,2}-inverses of matrices on Mn(F) if and only if f has one of the following forms: (a) f = 0; (b) f(A) = εPAτP-1 for any A ∈ Mn(F), where P ∈GLn(F), τ is some injective endomorphism on F with τ(1) = 1, and ε = ±1; (c) f(A) = εP(Aτ)TP-1 for any A ∈ Mn(F), where r, e and P are as in (b).

关 键 词：域 特征 加法映射 

分 类 号：O152[理学—数学]