Spectrahedral Shadow

A spectrahedral shadow is a vector space projection of a spectrahedron onto a coordinate subspace (Netzer and Sanyal 2015). It can be written as

where is a nonnegative integer and the real symmetric matrices have a common finite size. The vector space projection is taken without subsequently forming its topological closure. This is equivalent to admitting an exact finite semidefinite lift. Every spectrahedron is a spectrahedral shadow by taking . For example, projecting the closed unit disk onto its first coordinate gives the interval .