Orthogonal decomposition of tensor trains

In this paper, we study the problem of decomposing a given tensor into train such that tensors at vertices are orthogonally decomposable. When has length two, and decomposable two symmetric, recover decomposition by considering random linear combinations slices. Furthermore, if symmetric low-rank but not decomposable, show whitening procedure can transform orthogonal case. network three or more provide an algorithm for recovering them subject to some rank conditions. Finally, in case trains which necessarily reduces novel matrix multiplied diagonal matrices on either side. We compare solutions, one based Sinkhorn's theorem Procrustes' algorithm. conclude with multitude open problems multilinear algebra arose our study.