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In this paper we consider the weights of the global minimum variance portfolio (GMVP). The returns are assumed to follow a matrix elliptically contoured distribution, i.e., the returns are assumed to be neither independent nor normally distributed. A test for the general linear hypothesis is given. The distribution of the test statistic is derived under the null and the alternative hypothesis. It turns out that its distribution is invariant with respect to the type of the matrix elliptical distribution, i.e., the stochastic properties of the GMVP do not depend either on the mean vector or on the distributional assumptions imposed on asset returns. In an empirical study we analyze an international diversified portfolio.