Determining subspaces on which a matrix is nonnegative definite
type: Item
instance of: scholarly article
title: Determining subspaces on which a matrix is nonnegative definite
zbMATH Open document ID: 0753.15013
DOI: 10.1016/0024-3795(92)90289-M
published in: Linear Algebra and its Applications
publication date: 1992-09-27T00:00:00Z
review text: The author gives methods for finding a subspace \(L\) of \(R^ n\) of high dimension on which a given real symmetric \(n\times n\) matrix \(A\) is nonnegative (positive) definite. The subspace \(L\) is constructed as the intersection of some hyperplanes. The first method assumes that \(A\) has few negative (nonpositive) eigenvalues and selects the hyperplanes from a given collection which includes the coordinate planes. The second method finds a subspace \(L\) of maximal dimension. It proceeds by selecting some hyperplanes from the given collection and then successively constructing additional hyperplanes until a maximal \(L\) is determined. Both methods rely on inertia theory. In this process some new inertia results are derived. Test problems are also given.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 57564
zbMATH Keywords: nonnegative definite matrix
zbMATH Keywords: subspace
zbMATH Keywords: eigenvalues
zbMATH Keywords: inertia
zbMATH Keywords: Test problems
author: Hannu Väliaho
reviewed by: Prem Narain
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 57564