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We establish an identity for E f (Y) -E f (X), when X and Y both have matrixvariateskew-normal distributions and the function f fulfills some weakconditions. Thecharacteristic function of matrix variate skew normaldistribution is then derived. Finally,we make use of it to derive somenecessary and sucient conditions for the comparisonof matrix variateskew-normal distributions under six di erent orders, such as usualstochasticorder, convex order, increasing convex order, upper orthant order,directionallyconvex order and supermodular order.

An Identity for Expectations and Characteristic Function of Matrix  Variate Skew-normalDistribution with Applications to Associated Stochastic  Orderings