Maximum relative distance between real rank-two and rank-one tensors
1 : Max Planck Institute for Mathematics in the Sciences
2 : Max Planck Institute for Mathematics in the Sciences
We investigate the maximum distance of a rank-two tensor to rank-one tensors. An equivalent problem is
given by the minimal ratio of spectral and Frobenius norm of a tensor. For matrices the distance of a rank k
matrix to a rank r matrices is determined by its singular values, but since there is a lack of a fitting analog of
the singular value decomposition for tensors, this question is more difficult in the regime of tensors.