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Bad Projections of the PSD Cone

Algebraic Geometry 2021-02-25 v2 Computational Geometry Optimization and Control

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.

Keywords

Cite

@article{arxiv.2006.09956,
  title  = {Bad Projections of the PSD Cone},
  author = {Yuhan Jiang and Bernd Sturmfels},
  journal= {arXiv preprint arXiv:2006.09956},
  year   = {2021}
}

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18 pages