The (Hilbert metric) geometry of properly convex domains generalize real hyperbolic geometry. This generalization is far from the Riemannian notion of non-positive curvature, but they have some intriguing similarities. I will explore this connection from a coarse geometry viewpoint. The focus will be on Morse geodesics ("negatively curved directions", in a coarse sense) in properly convex domains. I will show that Morse-ness can be characterized entirely using linear algebraic data (i.e. singular values of matrices that track the geodesic). Further, I will discuss how this coarse geometric notion of Morse is related to the symmetric space geometry as well as the smoothness of boundary points. This is joint work with Theodore Weisman.