A note on the reverse order laws for {1, 2, 3}- and {1, 2, 4}-inverses of multiple matrix products

作者：Liu Xifu^*; Yang Hu

来源：Electronic Journal of Linear Algebra, 2011, 22: 620-629.

• Reverse order law
• Maximal and minimal ranks
• Generalized inverse
• Generalized Schur complement

Motivated by the equivalent conditions for the inclusions
A(n){1,2,i}...A(2){1,2,i}A(1){1,2,i} subset of (A(1)A(2)...A(n)){1,2,i} (i = 3,4)
presented in [B. Zheng and Z. Xiong. The reverse order laws for {1,2,3}- and {1,2,4}-inverses of multiple matrix products. Linear Multilinear Algebra, 58:765-782, 2010.], we show that for i is an element of {3,4},
A(n){1,2,i}...A(2){1,2,i}A(1){1,2,i} = (A(1)A(2)...A(n)){1,2,i}
is equivalent to
A(n){1,2,i}...A(2){1, 2,i}A(1){1,2,i} subset of (A(1)A(2)...A(n)){1,2,i}.

• 出版日期2011-6
• 单位重庆大学