  In this paper we consider the problem of defining transforms for signals on
directed graphs, with a specific focus on defective graphs where the
corresponding graph operator cannot be diagonalized. Our proposed method is
based on the Schur decomposition and leads to a series of embedded invariant
subspaces for which orthogonal basis are available. As compared to diffusion
wavelets, our method is more flexible in the generation of subspaces, but these
subspaces can only be approximately orthogonal.
