Unimodality conditions for Gaussian sums

In this correspondence multivariable sufficient conditions for the unimodality of Gaussian sums (normal mixtures) with two terms are given. The first corresponds to equal proportions and covariance matrices for
x \in R^{n}
while the second yields to a general mixture and
x \in R^{2}
. These conditions may be useful in proving nonhomogeneity of random vectors in the reduction of the number of terms encountered in specific non-Gaussian estimation or in the computation of MAP estimates.