关于两个矩阵之和逆阵的讨论

摘要

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.%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.