Let L_n be the n-dimensional second order cone. A linear map from R^m to R^n is called positive if the image of L_m under this map is contained in L_n. For any pair (n,m) of dimensions, the set of positive maps forms a convex cone. We construct a linear matrix inequality of size (n-1)(m-1) that describes this cone.
Laboratory Jean Kuntzmann (LJK), University Joseph Fourier, Grenoble, France, August 2007