Here the number $ d $ of subspaces that were joined with the tensor product is called the **degree** (or sometimes **order**) of $ T $.

Just as $ n_i $ was the dimension of the respective subspace $ \mathbb{R}^{n_i} $, it is also the **dimension of the $i$-th mode**

of $T$. The full **dimensions** of $T$ (note the plural), or equivalently the dimensions of the **tensor space** to which $T$ belongs, are given by the ordered $d$-tuple $(n_1, n_2, \dots, n_d)$.

With discrete sets $[n] = \{1,2,\dots,n\}$ we can alternatively define a tensor entrywise as: