We derive discrete norm representations associated with projections of
interpolation spaces onto finite dimensional subspaces. These norms are
products of integer and noninteger powers of the Gramian matrices
associated with the generating pair of spaces for the interpolation
space. We include a brief description of some of the algorithms which
allow the efficient computation of matrix powers. We consider in some
detail the case of fractional Sobolev spaces both for positive and
negative indices together with applications arising in preconditioning
techniques.
Several other applications are described.