| 关于域上矩阵广义逆的加法映射 |
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| 引用本文： | 张显,曹重光.关于域上矩阵广义逆的加法映射[J].数学学报,2004,47(5):1013-101. |
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| 作者姓名： | 张显 曹重光 |
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| 作者单位： | 黑龙江大学数学系,哈尔滨,150080 |
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| 基金项目： | 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) |
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| 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.
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| 关 键 词： | 域 特征 加法映射 |
| 文章编号： | 0583-1431(2004)05-1013-06 |
Additive Maps on Generalized Inverses of Matrices over Fields |
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| Xian ZHANG Chong Guang CAO.Additive Maps on Generalized Inverses of Matrices over Fields[J].Acta Mathematica Sinica,2004,47(5):1013-101. |
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| Authors: | Xian ZHANG Chong Guang CAO |
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| Institution: | Xian ZHANG Chong Guang CAO (Department of Mathematics, Heilongjiang University, Harbin 150080, P. R. China) |
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| Abstract: | 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). |
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| Keywords: | Fields Characteristic Additive map |
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