  Decompositions of higher-order tensors into sums of simple terms are
ubiquitous. We show that in order to verify that two tensors are generated by
the same (possibly scaled) terms it is not necessary to compute the individual
decompositions. In general the explicit computation of such a decomposition may
have high complexity and can be ill-conditioned. We now show that under some
assumptions the verification can be reduced to a comparison of both the column
and row spaces of the corresponding matrix representations of the tensors. We
consider rank-1 terms as well as low multilinear rank terms (also known as
block terms) and show that the number of the terms and their multilinear rank
can be inferred as well. The comparison relies only on numerical linear algebra
and can be done in a numerically reliable way. We also illustrate how our
results can be applied to solve a multi-label classification problem that
appears in the context of blind source separation.

Spectral Theory;Numerical Analysis;Numerical Analysis