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