The reverse order law for {1,2,3}-inverse and {1,2,4}-inverse of products of two matrices
Zhao Jian-li · Journal of Shandong University · 2011
The reverse order laws for {1,2,3}-inverse and {1,2,4}-inverse of product of two matrices are studied by applying the product singular value decomposition P-SVD and the characters of generalized inverse.The necessary and sufficient conditions of(AB){1,2,3}■ B{1,2,3}A{1,2,3} and(AB){1,2,4}■ B{1,2,4}A{1,2,4}are obtained.Then equivalent conditions of(AB){1,2,3}=B{1,2,3}A{1,2,3} and(AB){1,2,4}=B{1,2,4}A{1,2,4} are obtained.