I have to prove that $\max\limits_{t \in \mathbb{R}^{n\times m\times k}} brk (t) \ge \max(\min(n, mk), \min(m, nk), \min(k, nm))$, where $brk(t)$ is the border rank of $t$.
I suppose that it is well-known statement but I am just starting to learn tensors and do not know how to prove this. Of course because of symmetry it is sufficient to prove that $\max\limits_{t \in \mathbb{R}^{n\times m\times k}} brk (t) \ge \min(n, mk)$. Maybe we can just give an example of such sequence?
Thanks for the help!