Further Results on the Reverse Order Law for {1,3}-Inverse and {1,4}-Inverse of a Matrix Product

Abstract

Both Djordjević (2007) and Takane et al. (2007) have studied the equivalent conditions for B{1,3}A{1,3}⊆(AB){1,3} and B{1,4}A{1,4}⊆(AB){1,4}. In this note, we derive the necessary and sufficient conditions for B{1,3}A{1,3}⊇(AB){1,3}, B{1,4}A{1,4}⊇(AB){1,4}, B{1,3}A{1,3}=(AB){1,3} and B{1,4}A{1,4}=(AB){1,4}.