Generalized inverse restricted by the normal Drazin equation

Abstract

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