摘要
定义了两个矩阵乘积关于广义逆的交换律与广义交换律的概念,利用矩阵秩方法及奇异值分解分别研究了两个矩阵乘积关于{1}-逆,{1,2}-逆,{1,3}-逆与{1,4}-逆的交换律与广义交换律成立的充要条件,并对其进行了比较.
The concepts of the commutative laws and generalized commutative laws of matrix multiplication on generalized inverse were defined.Using the matrix rank method and SVD,necessary and sufficient conditions about the commutative laws and generalized commutative laws of matrix multiplication on{1}-inverse,{1,2}-inverse,{1,3}-inverse and{1,4}-inverse were established respectively,and these conditions were compared between themselves.
作者
李莹
高岩
郭文彬
LI Yin;GAO Yan;GUO Wen-bin(Business School,University of Shanghai for Science and Technology,Shanghai 200093,China;College of Mathematics Science,Liaocheng University,Liaocheng 252059,China)
出处
《上海理工大学学报》
CAS
北大核心
2011年第4期379-383,共5页
Journal of University of Shanghai For Science and Technology
基金
国家自然科学基金资助项目(11171221)
关键词
{i
j
k}-逆
群逆
广义SCHUR补
秩方法
奇异值分解
交换律
{i,j,k}-inverse
group inverse
generalized Schur complement
matrix rank method
singular value decomposition
commutative laws
