Weighted extended core inverseMosić, Dijana (Avtor) Marovt, Janko (Avtor) Extended core inverseW-weighted core–EP inversecore inverseWg–Drazin inverseThe extended core inverse was presented for square complex matrices as an extension of the core inverse based on the sum and difference of known generalized inverses. Unlike of existing generalizations of the core inverse, the extended core inverse is an inner inverse of the matrix which need not necessarily be the null matrix of a nilpotent matrix. The aim of this paper is to consider a generalization of the system for defining the extended core inverse based on a weight and to introduce a weighted extended core inverse for operators between two Hilbertspaces. Thus, we consider a new type of weighted generalized inverses. Properties, characterizations and expressions for the weighted extended core inverse are established. The dual version of the weighted extended core inverse is studied too and it presents a new extension of the Moore-Penrose inverse. We apply the weighted extended core inverse and its dual to solve certain systems of linear equations and minimization problems.20262026-07-30 09:17:14Znanstveno delo99082sl