For Peer Review Only Generalized inverse restricted by the normal

In this work we introduce a new kind of generalized inverse, called the T-restricted weighted Drazin inverse of A with respect to a positive semidefinite/definite matrix T. The new approach proposed makes use of the normal Drazin equation of a non consistent matrix equation as the constraint set of the minimization. In addition, when T is positive semidefinite, the minimal seminorm solution is considered for all vectors belonging to N (T)⊥. We also show that the solution of the problem can be represented as a particular outer inverse solution