  The problem of estimating a mean matrix of a multivariate complex normal
distribution with an unknown covariance matrix is considered under an invariant
loss function. By using complex versions of the Stein identity, the Stein-Haff
identity, and calculus on eigenvalues, a formula is obtained for an unbiased
estimate of the risk of an invariant class of estimators, from which several
minimax shrinkage estimators are constructed.
