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Bad Projections of the PSD Cone
Published 17 Jun 2020 in math.AG, cs.CG, and math.OC | (2006.09956v2)
Abstract: The image of the cone of positive semidefinite matrices under a linear map is a convex cone. Pataki characterized the set of linear maps for which that image is not closed. The Zariski closure of this set is a hypersurface in the Grassmannian. Its components are the coisotropic hypersurfaces of symmetric determinantal varieties. We develop the convex algebraic geometry of such bad projections, with focus on explicit computations.
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