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The multilinear normal distribution is a widely used tool in tensor analysisof magnetic resonance imaging (MRI). Diffusion tensor MRI provides astatistical estimate of a symmetric 2nd-order diffusion tensor, for each voxelwithin an imaging volume. In this article, tensor elliptical (TE) distributionis introduced as an extension to the multilinear normal (MLN) distribution.Some properties including the characteristic function and distribution ofaffine transformations are given. An integral representation connectingdensities of TE and MLN distributions is exhibited that is used in deriving theexpectation of any measurable function of a TE variate.

Some theoretical results on tensor elliptical distribution