  We provide a general theoretical framework to derive Bernstein-von Mises
theorems for matrix functionals. The conditions on functionals and priors are
explicit and easy to check. Results are obtained for various functionals
including entries of covariance matrix, entries of precision matrix, quadratic
forms, log-determinant, eigenvalues in the Bayesian Gaussian
covariance/precision matrix estimation setting, as well as for Bayesian linear
and quadratic discriminant analysis.
