Parameter-free description of the manifold of non-degenerate density matrices

The paper gives a definition of exponential arcs in the manifold non-degenerate density matrices and uses it as starting point to develop parameter-free version non-commutative Information Geometry finite-dimensional case. Given Bogoliubov metric m- e-connections are each other dual. Convex potentials introduced. They allow introduce dual charts. Affine coordinates introduced at end make connection with more usual approach.