Determinantal representations of weighted Moore-Penrose inverse

Abstract

In this paper we introduce determinantal representation of {ıt weighted Moore-Penrose inverse\/} of a rectangular matrix. We generalize concept of generalized algebraic complement, introduced by Moore, Arghiriade, Dragomir and Gabriel. This extension is denoted as weighted generalized algebraic complement. Moreover, we derive an explicit determinantal representation for the weighted least-squares minimum norm solution of a linear system and prove that this solution lies in the convex hull of the solutions to the square subsystems of the original system.