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Bad Projections of the PSD Cone

06/17/2020

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by Yuhan Jiang, et al.

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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.

Yuhan Jiang
4 publications
Bernd Sturmfels
38 publications

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