Mixed-type reverse order laws for {1,2,3}-inverse and {1,2,4}-inverse of products of two matrices
Wenbin Guo · Journal of the University of Shanghai for Science and Technology · 2010
Mixed-type reverse order laws for {1,2,3}-inverse and {1,2,4}-inverse of product of two matrices were studied by use of maximal and minimal ranks of generalized Schur complement.The necessary and sufficient conditions of unilateral inclusion relation {B(1,2,3)(ABB(1,2,3))(1,2,3)}■{(AB)(1,2,3)} and {A(1,2,3)AB)(1,2,3)A(1,2,3)}■{(AB)(1,2,3)} were obtained,similarly equivalent conditions of {B(1,2,4)(ABB(1,2,4))(1,2,4)}■{(AB)(1,2,4)} and {A(1,2,4)AB)(1,2,4)A(1,2,4)}■{(AB)(1,2,4)} were achieved.