Bad Projections of the PSD Cone

2020/06/17 by Yuhan Jiang, Bernd Sturmfels, Jiang, Yuhan +1 · 2 citations
Physics and Astronomy · #Advanced Fiber Laser Technologies #Algebraic Geometry (math.AG) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2006.09956

openalex publication_date 2020/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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