| 关于两个矩阵之和逆阵的讨论 |
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| 引用本文： | 周梦,张玉俊.关于两个矩阵之和逆阵的讨论[J].大学数学,2011,27(5):149-151. |
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| 作者姓名： | 周梦 张玉俊 |
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| 作者单位： | 1. 北京航空航天大学数学与系统科学学院,LMIB,北京100083
2. 河北北方学院数学系,河北张家口,075000 |
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| 摘 要： | 在数域F上的n阶矩阵环中讨论两个矩阵之和的逆阵（A＋B）-1与矩阵A,B之逆A-1,B-1的关系,给出复数域和实数域上等式（A＋B）-1=A-1＋B-1成立的充要条件.
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| 关 键 词： | 矩阵之和 逆矩阵 复相似 实相似 若当标准形 |
On the Inverse of Sum of Two Matrices |
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| ZHOU Meng,ZHANG Yu-jun.On the Inverse of Sum of Two Matrices[J].College Mathematics,2011,27(5):149-151. |
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| Authors: | ZHOU Meng ZHANG Yu-jun |
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| Institution: | ZHOU Meng1,ZHANG Yu-jun2(1.School of Mathematics and System Science,Beihang University,Beijing 100083,China,2.Department of Mathematics,Hebei North University,Zhangjaikou 075000,China) |
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| Abstract: | This paper discusses the relationship between the inverse （A＋B）^-1 of sum of two matrix A,B and A^-1 , B^-1, the inverse of matrix A,B. As main results, the conditions for equation （A＋B）^-1 =A^-1 ＋B^-1 on complex number field and real number field are given in this paper. |
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| Keywords: | sum of matrices inverse of matrix similar on complex number field similar on real number field Jordan canonical form |
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