In this paper, we introduce a new domain adaptation (DA) algorithm where the source and target domains are represented by subspaces described by eigenvectors. In this context, our method seeks a domain invariant feature space by learning a mapping function which aligns the source subspace with the target one. We show that the solution of the corresponding optimization problem can be obtained in a simple closed form, leading to an extremely fast algorithm. We use a theoretical result to tune the unique hyperparameter corresponding to the size of the subspaces. We run our method on various datasets and show that, despite its intrinsic simplicity, it outperforms state of the art DA methods.