A Hankel tensor is a symmetric tensor whose entries depend only on the sum of their indices (Qi 2015). For order 
and dimension 
, this means that there are scalars 
, 
, ..., 
such that
 |
for 
. Permuting the indices preserves their
sum, which explains the symmetry. The case 
is a Hankel matrix. Real
and complex decompositions can have different ranks.
