We give a sucient condition for strictly positive def- initeness in Rd. The result is based on the question how sparse subsets of Rd can be to guarantee linear independence of the ex- ponentials. Interpolation by positive definite functions has become a widely used technique in approximation theory and spatial statistics. The basic model is defined as linear combination of translates of a given positive definite function, called basis function. Setting up the collocation ma- trix for the problem, one has to assume the matrix to be invertible. This is guaranteed if the basis function is assumed to be strictly posi- tive definite. Hereby, a function ' : Rd ! C is called strictly positive definite if for arbitrary dierent points