\indent the space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. many books and papers have been written on this subject, and more recently there has been considerable interest in high- dimensional random matrices with particular emphasis on the distribution of certain eigenvalues. our present paper is motivated by modern data acquisition technology, particularly, by the availability of diffusion tensor-magnetic resonance data. with the availability of such data acquisition capabilities, smoothing or nonparametric techniques are required that go beyond those applicable only to data arising in euclidean spaces. accordingly, we present a fourier method of minimax wishart mixture density estimation on the space of positive definite symmetric matrices.