Bad projections of the PSD cone

• Jiang, Yuhan ^[1] ; Sturmfels, Bernd ^[2]
  1. [1] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     
  2. [2] Max Planck Institute for Mathematics in the Sciences

     Max Planck Institute for Mathematics in the Sciences

     Kreisfreie Stadt Leipzig, Alemania

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 72, Fasc. 2, 2021, págs. 261-280
• Idioma: inglés
• DOI: 10.1007/s13348-021-00319-4
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• Resumen

  • 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.