&= \sum_{j_1=1}^{n_1} \cdots \sum_{j_{k-1}=1}^{n_{k-1}} \sum_{j_{k+1}=1}^{n_{k+1}} \cdots \sum_{j_d=1}^{n_d} \mathbf{e}_{j_1}^1 \otimes \cdots \otimes \mathbf{e}_{j_{k-1}}^{k-1} \otimes M_k \left ( \sum_{j_k=1}^{n_k} a_{j_1,j_2,\ldots,j_d} \mathbf{e}_{j_k}^k \right) \otimes \mathbf{e}_{j_{k+1}}^{k+1} \otimes \cdots \otimes \mathbf{e}_{j_d}^d.
