Generalization of the Hilbert metric to the space of positive definite matrices by Carlangelo Liverani and Maciej P. Wojtkowski ABSTRACT We introduce a generalization of the Hilbert projective metric to the space of positive definite matrices which we view as part of the Lagrangian Grassmannian. PUBLISHED ON Pacific Journal of Mathematics, 166, N.2, pp. 339-355, (1994).