Projective norms are capable of measuring entanglement of multipartite quantum states. However, typically, the explicit computation of these distancebased geometric entanglement monotones is very difficult even for finite dimensional systems. Motivated by the significance of Schmidt decompositions for our quantitative understanding of bipartite quantum entanglement, a generalization of this concept to multipartite scenarios is proposed, in the sense that generalized Schmidt decomposability of a

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... multipartite pure state implies that its projective norm can be calculated in a simple way analogous to the bipartite case. Thus, this concept of generalized Schmidt decomposability of multipartite quantum states is linked in a natural way to projective norms as entanglement monotones. Therefore, it may not only be a convenient tool for calculations, but may also shed new light onto the intricate features of multipartite entanglement in an analogous way as the 'classical' Schmidt decomposition does for bipartite quantum systems.