If an ordered point configuration in projective space is represented by a matrix of coordinates, the resulting matrix is determined up to the action of the general linear group on one side and the torus of diagonal matrices on the other. We study orbits of matrices under the action of the product of these groups, as well as their images in quotients of the space of matrices like the Grassmannian. The main question is what properties of closures of these orbits are determined by the matroid of the point configuration; the main result is that their equivariant K-classes are so determined. I will also draw connections to positivity and the work of Berget, Eur, Spink and Tseng.