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Diagonalizability, orthogonal diagonalizability of higher order tensors and their being or not being dense in some suitable topology

For our discussion, we'll assume that we're working with $\mathbb{R}^m$ only, but much or all of the following discussion should be carried over immediately to any finite dimensional inner product ...
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Tensor nuclear norm for a binary 3rd-order tensor

I am interested in the low-rank approximation of a binary(01) third-order tensor. Does anyone know how to define its tensor nuclear norm based on whatever tensor decomposition methods? Could anyone ...