Semialgebraic Geometry of Nonnegative Tensor Rank
Semialgebraic Geometry of Nonnegative Tensor Rank
We study the semialgebraic structure of $D_r$, the set of nonnegative tensors of nonnegative rank not more than $r$, and use the results to infer various properties of nonnegative tensor rank. We determine all nonnegative typical ranks for cubical nonnegative tensors and show that the direct sum conjecture is true …