\(Z\) \(\sim\) Inverted Wishart(nu,V).
In this parameterization, \(E[Z] = 1/(nu-k-1) V\), where \(V\) is a \(k x k\) matrix lndIWishart computes the complete log-density, including normalizing constants.
References
For further discussion, see Chapter 2, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.