Two perhaps ill-posed or just silly questions:

- Let $n>0$, $T$ be an $(n+2)$-tensor, and $\otimes$ denote the Kronecker product of tensors. Is there a tensor generalization for the fundamental eigenvector-eigenvalue relationship $M\cdot v_k - \lambda_k v_k = 0$ of the form: $$T \otimes T'_k = T''_k \otimes T'_k,$$ where $T'_k$ is an $(n+1)$-tensor, $T''_k$ is an $n$-tensor, and $k\in\mathbb Z^{n+1}$?
- If [1] is not silly, does this structure form a hierarchy for decomposing $T$ into sums/products of such $(n+1)$- and $n$-tensors $T'_k$ and $T''_k$? My apologies for bad notation. Thank you for your comments.