Moore-Penrose inverses of Gram matrices
leaving a cone invariant in an indefinite inner
product space

We classify, extend and unify various generalizations of weighted Moore-Penrose inverses in indefinite inner product spaces. New kinds of generalized inverses are introduced for this purpose. These generalized inverses are included in the more general class called as the weighted indefinite pseudoinverses (WIPI), which represents an extension of the Minkowski inverse (MI), the weighted Minkowski inverse (WMI), and the generalized weighted Moore-Penrose (GWM-P) inverse. The WIPI generalized inverses are introduced on the basis of two Hermitian invertible matrices and two Hermitian involuntary matrices and represented as particular outer inverses with prescribed ranges and null spaces, in terms of appropriate full-rank and limiting representations. Application of introduced generalized inverses in solving some indefinite least squares problems is considered. New Zeroing Neural Network (ZNN) models for computing the WIPI are developed using derived full-rank and limiting representations. The convergence behavior of the proposed ZNN models is investigated. Numerical simulation results are presented.

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Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space

Abstract: Abstract:In this paper we characterize Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space using the indefinite matrix multiplication. This characterization includes the acuteness (or obtuseness) of certain closed convex cones.

Cited by 2 publications

References 15 publications

A Method of Indefinite Krylov Subspace for Eigenvalue Problem

A Method of Indefinite Krylov Subspace for Eigenvalue Problem

Complex ZNN for computing time-varying weighted pseudo-inverses

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