A Note on the Convex Hull of Finitely Many Projections of Spectrahedra

Tim Netzer; Rainer Sinn

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arXiv · 0908.3386

A Note on the Convex Hull of Finitely Many Projections of Spectrahedra

Tim Netzer·Rainer Sinn

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Abstract

A spectrahedron is a set defined by a linear matrix inequality. A projection of a spectrahedron is often called a semidefinitely representable set. We show that the convex hull of a finite union of such projections is again a projection of a spectrahedron. This improves upon the result of Helton and Nie, who prove the same result in the case of bounded sets.

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Tim Netzer, Rainer Sinn. 2009-08-24. A Note on the Convex Hull of Finitely Many Projections of Spectrahedra. https://arxiv.org/abs/0908.3386

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