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

摘要

Both Djordjevic (2007) and Takane et al. (2007) have studied the equivalent conditions for B{1,3}A{1,3} C (AB){1,3} and B{1,4}A{1,4} C (AB){1,4}. In this note, we derive the necessary and sufficient conditions for B{1,3}A{1,3) 2 (AB){1,3}, B(1,4)A{1,4) 2 (AB){1,4}, B{1,3}A{1,3} = (AB){1,3} and B{1,4}A{1,4} = (AB){1,4}.