Abstract:

The reverse order laws for ｛1,2,3｝-inverse and ｛1,2,4｝-inverse of product of two matrices have been 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.

Key words: reverse order law; Generalized inverse; P-SVD