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.