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Determinantal representation of weighted Moore-Penrose inverse. (English) Zbl 0840.15005
Summary: We introduce a determinantal representation of the weighted Moore-Penrose inverse of a rectangular matrix. We generalize the concept of the 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.

MSC:
15A09 Theory of matrix inversion and generalized inverses
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
15A06 Linear equations (linear algebraic aspects)
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