There is an obvious, though not canonical, way to record the data of a hyperplane arrangement in projective space as a matrix of coefficients. Our protagonist in this talk is the closure of the set of matrices describing a given arrangement. We discuss formulae for certain invariants of this variety which depend on the underlying matroid alone, giving support for the conjecture that its equivariant Hilbert series has such a formula. This talk includes joint work with David Speyer and with Andrew Berget.