Summary: Let X be an \(m\times p\) matrix normally distributed with matrix of means B and covariance matrix \(I_ m\otimes \Sigma\), where \(\Sigma\) is a \(p\times p\) unknown positive definite matrix. This paper studies the estimation of B relative to the invariant loss function \[ tr \Sigma^{- 1}(\hat B-B)^ t(\hat B-B). \] New classes of invariant minimax estimators are proposed for the case \(p>m+1\), which are multivariate extensions of the estimators of Stein and Baranchik. The method involves the unbiased estimation of the risk of an invariant estimator which depends on the eigenstructure of the usual \(F=XS^{-1}X^ t\) matrix, where S: \(p\times p\) follows a Wishart matrix with n degrees of freedom and mean \(n\Sigma\).