The Forward Order Law for Least Squareg-Inverse of Multiple Matrix Products
The Forward Order Law for Least Squareg-Inverse of Multiple Matrix Products
复制标题
DOI：
10.3390/math7030277
复制
发表时间：
2019-03
期刊：
影响因子：
2.4
通讯作者：
Zhiping Xiong;Zhongshan Liu
中科院分区：
文献类型：
--
作者：
Zhiping Xiong;Zhongshan Liu
广义逆在矩阵和统计学的理论研究中有许多重要的应用。广义逆的核心问题之一是求矩阵乘积的广义逆的正序律的充要条件。利用广义Schur补的极值秩导出了正序律A1{1，3}A2{1，3}⋯An{1，3}⊆(A1A2⋯An){1，3}和A1{1，4}A2{1，4}⋯An{1，4}⊆(A1A2⋯An){1，4}的一些充要条件.
The generalized inverse has many important applications in the aspects of the theoretic research of matrices and statistics. One of the core problems of the generalized inverse is finding the necessary and sufficient conditions of the forward order laws for the generalized inverse of the matrix product. In this paper, by using the extremal ranks of the generalized Schur complement, we obtain some necessary and sufficient conditions for the forward order laws A 1 { 1 , 3 } A 2 { 1 , 3 } ⋯ A n { 1 , 3 } ⊆ ( A 1 A 2 ⋯ A n ) { 1 , 3 } and A 1 { 1 , 4 } A 2 { 1 , 4 } ⋯ A n { 1 , 4 } ⊆ ( A 1 A 2 ⋯ A n ) { 1 , 4 } .