Best subspace tensor approximations: a quantum physical interpretation

We will comment on a recent work by S. Friedland and V. Mehrmann\\ (http://arxiv.org/abs/0805.4220), where the authors generalize the singular value decomposition method to obtain low-rank approximation of tensors. In particular, we will explain the underlying quantum physical concepts behind their proposed best subspace approximations as well as generalisations of these concepts to symmetric and exterior algebra elements. Illustrations will be taken from the field of quantum chemistry.