Abstract
A binary tensor consists of 2 (n) entries arranged into hypercube format 2 × 2 × ⋯ × 2. There are n ways to flatten such a tensor into a matrix of size 2 × 2 (n-1). For each flattening, M, we take the determinant of its Gram matrix, det(MM(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.