Reverse Order Law for the Weighted Drazin Inverse of a Matrix Right Semi-tensor Product
Jianli Zhao · Journal of Huaihai Institute of Technology · 2009
The rank methods of matrix are used to study the reverse order law for the generalized inverse of the matrices right semi-tensor product.Let(Bd,W2Ip)*Ad,W1=(Bd,W2Ip)W2W1Ad,W1 be given.At the same time,a sufficient and necessary condition for the weighted Drazin inverse(A⊙B)d,I=(Bd,W2Ip)*Ad,W1 is given.Particularly,as matrix A and matrix B are square matrices,and matrix W1 and matrix W2 are identity matrices,a sufficient and necessary condition can be obtained directly for(A⊙B)d=(BdIp)Ad to hold the Drazin inverse.