What is the entropy of the Inverse-Wishart distribution? I need just a reference, but derivation (e.g. using inverse property) would be interesting too.

**Answer**

### Wishart and Inverse Wishart Distributions

The Wishart and inverse Wishart distributions are arguably the most popular distributions for modeling random positive definite matrices. Moreover, if a random variable has a Gaussian distribution, then its sample covariance is drawn from a Wishart distribution. The relative entropy between Wishart distributions may be a useful way to measure the dissimilarity between collections of covariance matrices or Gram (inner product) matrices.

A new Bayesian entropy estimator is proposed using an inverted Wishart distribution and a data-dependent prior that handles the small-sample case.

### Inverse Wishart Differential Entropy and Relative Entropy

The above link explains the derivation of the entropy of Inverse-Wishart distribution

**Attribution***Source : Link , Question Author : sbos , Answer Author : Pluviophile*