Given a tensor $T$ with a tensor decomposition  $\sum _{i=1}^r{T}_{i1}\otimes T_{i2}\otimes T_{i3}$ of $T$, where each summand is a rank-one tensor:

• the integer $r$ is the tensor decomposition rank of the tensor decomposition $T$;

• the ordered list ${\left[{\left(rank{T}_{ij}\right)}_{j=1\cdots 3}\right]}_{i=1\cdots r}$ is called the type of the tensor decomposition of $T$ (where $rankM$ denotes the classical rank of the matrix $M$).

The type can be summarized as the multivariate polynomial $\sum _{i=1}^r{X}^{rank{T}_{i1}}{Y}^{rank{T}_{i2}}{Z}^{rank{T}_{i3}}$.