I'm completely new in this field of algebra and I would like to better understand the extension of the SVD in the multilinear case. In particular, I'm interested in understanding what the so-called "score subspace" is in this setting. In the matrix case, suppose I have $A$, the SVD is:
$$A=U\Sigma V^T$$
I'm used to call $row(A)$the score subspace of $A$, which is spanned by the right singular vectors in $V$.
How this concept is extended in the High Order SVD?
Thanks in advance