  We consider finite-dimensional Bayesian linear inverse problems with Gaussian
priors and additive Gaussian noise models. The goal of this note is to present
a simple derivation of the well-known fact that solving the Bayesian D-optimal
experimental design problem, i.e., maximizing the expected information gain, is
equivalent to minimizing the log-determinant of posterior covariance operator.
We focus on finite-dimensional inverse problems. However, the presentation is
kept generic to facilitate extensions to infinite-dimensional inverse problems.
