反序律B｛1,2,i｝A｛1,2,i｝=(AB)｛1,2,i｝i=3,4成立的充要条件  

Necessary and sufficient conditions for reverse order laws B{1,2,i}A{1,2,i}■(AB){1,2,i},i=3,4

作　　者：孙萍[1] 孟令胜[2] 

机构地区：[1]乌鲁木齐职业大学基础部,新疆乌鲁木齐830002 [2]兰州交通大学博文学院,甘肃兰州730000

出　　处：《兰州理工大学学报》2011年第3期167-172,共6页Journal of Lanzhou University of Technology

摘　　要：证明两个矩阵乘积的{1,2,3}-逆和{1,2,4}-逆反序律包含关系B{1,2,i}A{1,2,i}■(AB){1,2,i},i=3,4分别等价于等式反序律B{1,2,i}A{1,2,i}=(AB){1,2,i},i=3,4.从而得到上述等式反序律成立的充要条件.It was verified that the inclusion relationship B{1,2,i}A{1,2,i}lohtain in（AB）{1,2,i},i=3,4 for reverse order laws of {1,2,3}-inverse and {1,2,4}-inverse of the product of two matrixes was respectively equivalent to the identical reverse order laws B{1,2,i}A{1,2,i}=（AB）{1,2,i},i=3,4,so that the necessary and sufficient conditions were obtained for holding the foregoing identical reverse order laws.

关 键 词：反序律 广义逆 极大秩 极小秩 广义SCHUR补 

分 类 号：O151.21[理学—数学]