Comon's Conjecture, Rank Decomposition, and Symmetric Rank Decomposition of Symmetric Tensors

Bounds on the tensor rank

“…We show that Corollary 3.10 provides new evidences for the Comon's Conjecture, sometimes even in a numerical range larger than the ones considered in previous works on the topic (e.g. [F16] and [ZHQ16]).…”

On approximate diagonalization of third order symmetric tensors by orthogonal transformations

“…We present a counterexample to these equivalent problems based on the decomposition of orthogonal matrices. Moreover, we prove a result that can be seen as an orthogonal analogue of the so-called Comon's Conjecture [18]. The second goal of this paper is to study the convergence properties of the original Jacobi CoM2 algorithm [11].…”

Decomposability of Tensors

“…The question raised by Comon asks if whether such an inequality is actually an equality. Affirmative answers were given in several cases (see [176][177][178][179][180]). In [181], Shitov found an example (a cubic in 800 variables) where the inequality (29) is strict.…”