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.

中文翻译：

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PSD 锥体的错误投影

线性映射下正半定矩阵的锥体的图像是凸锥体。Pataki 表征了该图像未闭合的线性映射集。该集合的 Zariski 闭包是 Grassmannian 中的超曲面。它的组成部分是对称行列簇的各向同性超曲面。我们开发了这种糟糕投影的凸代数几何，重点是显式计算。