Suppose we have a 4-index tensor $t_{ijkl}$ (all 4 dimensions are equal size). We can make a matrix out of it by taking first and last two indexes as new indexes: $t_{ijkl} \rightarrow M_{ij, kl}$. Suppose we have an SVD of this matrix $M = U S V^\dagger$. Now we take another matricization of $t$, such that $t_{ijkl} \rightarrow N_{ik, jl}$. Can we say anything about the SVD of $N$ from the SVD of $M$? Can the SVD of $N$ be calculated using the SVD of $M$?