  We develop singular value shrinkage priors for the mean matrix parameters in
the matrix-variate normal model with known covariance matrices. Our priors are
superharmonic and put more weight on matrices with smaller singular values.
They are a natural generalization of the Stein prior. Bayes estimators and
Bayesian predictive densities based on our priors are minimax and dominate
those based on the uniform prior in finite samples. In particular, our priors
work well when the true value of the parameter has low rank.
