大学数学
大學數學
대학수학
COLLEGE MATHEMATICS
2011年
5期
149-151
,共3页
矩阵之和%逆矩阵%复相似%实相似%若当标准形
矩陣之和%逆矩陣%複相似%實相似%若噹標準形
구진지화%역구진%복상사%실상사%약당표준형
sum of matrices%inverse of matrix%similar on complex number field similar on real number field%Jordan canonical form
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.
在數域F上的n階矩陣環中討論兩箇矩陣之和的逆陣（A＋B）-1與矩陣A,B之逆A-1,B-1的關繫,給齣複數域和實數域上等式（A＋B）-1=A-1＋B-1成立的充要條件.
재수역F상적n계구진배중토론량개구진지화적역진（A＋B）-1여구진A,B지역A-1,B-1적관계,급출복수역화실수역상등식（A＋B）-1=A-1＋B-1성립적충요조건.
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.
