Determining subspaces on which a matrix is nonnegative definite (Q1189625)

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.