If so can such a formalism give us extra rich structures, in some way. Or can such systems be essentially shown to be equivalent to 2d matrices, or some other structure on V$ \mathbb{x}$ V ?
2026-03-29 08:44:27.1774773867
Can the concept of matrices be extended to include 3d tuples (3d arrays)?
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Here is an article about eigenvectors for tensors: Tensors and their Eigenvectors. It talks about decomposing tensors into sums of rank 1 tensors, singular value decomposition etc.
Sorry this doesn't qualify as answer and thus should be a comment, but I don't have enough reputation to do so.