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}
}
Comments
18 pages