This is an introductory survey, from a geometric perspective, on the Singular Value Decomposition (SVD) for real matrices, focusing on the role of the Terracini Lemma. We extend this point of view to tensors, we define the singular space of a tensor as the space spanned by singular vector tuples and we study some of its basic properties.

Sia X $\subset\mathbf{P^{\textrm{n}}}$ una varietà di codimensione 2. Proviamo che H$^{q}$($\mathcal{I}_{x}(t))$=0 per n$\geq$q +4t+3, e 1$\leq q\leq n-2$