What Determines the Rank of a 2x2x2 Tensor?

[tolearn]

Rank of a tensor--- 2x2x2 Array

Can anybody give me an example of 2x2x2 Array whose tensor rank is 2

or

Can somebody show me why the tensor rank is two for the following 2x2x2 array. That is can you express as a sum of 2 outer products?
I am giving the entries of the first face and then the second face. I do realize I could have asked this question various other terminology--this is the one I am most comfortable one. I hope my question is clear. Thank you

1 0 0 1
01 1 0

 

[fresh_42]

The rank of a $(2,2,2)-$tensor $T$ is the minimum $m\in \mathbb{N}_0$ such that there is an representation
$$
T=\sum_{k=1}^m u_k \otimes v_k \otimes w_k
$$
Thus you have just to make sure, that all $u_k,v_k,w_k$ are "sufficiently" linearly independent:
$$
T:= \begin{bmatrix}1\\0\end{bmatrix}\otimes \begin{bmatrix}0\\1\end{bmatrix}\otimes \begin{bmatrix}a\\b\end{bmatrix} + \begin{bmatrix}0\\1\end{bmatrix}\otimes \begin{bmatrix}1\\0\end{bmatrix}\otimes \begin{bmatrix}c\\d\end{bmatrix}
$$
Here is an $(4,4,4)-$example: https://www.physicsforums.com/insights/what-is-a-tensor/