Application of Matrix Rank Methods in the Reverse Order Law of the Generalized Inverse Matrix
Liu Ding-you · 2010
One of the major shortcomings of the Moor-penrose inverse is that the 'reverse order law' does not always hold,that is,(AB)+ is not always equal to B+A+.Some scholars used the theory of projection to discuss this issue.They got a number of necessary and sufficient conditions on(AB)+=B+A+.In this paper,matrix rank methods are used to discuss the 'reverse order law' on Moor-penrose.The proof becomes more concise.