  A binary tensor consists of $2^n$ entries arranged into hypercube format $2
\times 2 \times \cdots \times 2$. There are $n$ ways to flatten such a tensor
into a matrix of size $2 \times 2^{n-1}$. For each flattening, $M$, we take the
determinant of its Gram matrix, ${\rm det }(M M^T)$. We consider the map that
sends a tensor to its $n$-tuple of Gram determinants. We propose a
semi-algebraic characterization of the image of this map. This offers an answer
to a question raised by Hackbusch and Uschmajew concerning the higher-order
singular values of tensors.
