Is there a more efficient way to calculate A * A.transpose(), where A is a Eigen matrix?

You can use a SelfAdjointView to compute only half of the product. This will provide gain only if A is not too small:

res.setZero(n,n);
res.selfadjointView<Lower>.rankUpdate(A);

This will compute only the lower half. This is enough for solving with Cholesky or applying products trough the selfadjointView. To get a full matrix:

res.triangularView<StrictUpper>() = res.adjoint().triangularView<StrictUpper>();