  The image of a linear space under inversion of some coordinates is an affine
variety whose structure is governed by an underlying hyperplane arrangement. In
this paper, we generalize work by Proudfoot and Speyer to show that circuit
polynomials form a universal Groebner basis for the ideal of polynomials
vanishing on this variety. The proof relies on degenerations to the
Stanley-Reisner ideal of a simplicial complex determined by the underlying
matroid. If the linear space is real, then the semi-inverted linear space is
also an example of a hyperbolic variety, meaning that all of its intersection
points with a large family of linear spaces are real.
