 If formula_14 and formula_15 is of size formula_16, then formula_17 has an inverse Wishart distribution formula_18 .Suppose formula_19 has an inverse Wishart distribution.Partition the matrices formula_20 and formula_21 conformably with each other 
where formula_23 and formula_24 are formula_25 matrices, then we have

i) formula_26 is independent of formula_27 and formula_28, where formula_29 is the Schur complement of formula_30 in formula_20;

ii) formula_32;

iii) formula_33, where formula_34 is a matrix normal distribution;

iv) formula_35, where formula_36;

Suppose we wish to make inference about a covariance matrix formula_37 whose prior formula_38 has a formula_39 distribution.