A comment on some recent results concerning the reverse order law for {1, 3, 4}-inverses

摘要

This paper has been motivated by the one of Liu and Yang [D. Liu, H. Yang, The reverse order law for {1, 3, 4}-inverse of the product of two matrices, Appl. Math. Comp. 215 (12) (2010) 4293–4303] in which the authors consider separately the cases when and , where and . Here we prove that is actually equivalent to . We show that can only be possible if and in this case, we present purely algebraic necessary and sufficient conditions for this inclusion to hold. Also we give some new characterizations of .