Computing the Inverse of a Cubic Matrix

[Bruno Tolentino]

Be the matrix A defined by [a_ijk] (a matrix 2x2x2), do you know how to compute a inverse this cubic matrix?

 

[Orodruin]

First you would need to define what you mean by the inverse of a cubic matrix.

 

[WWGD]

Is the cubic matrix (the representation of ) a 3-linear map? If so, then it is a 3-tensor. I don't think there is a notion of invertibility for k-tensors, but I am not sure.

 

[Bruno Tolentino]

The inverse of a cubic matrix is for try to solve a system of conic equation, like this:

I think that the solution could have the same form that quadratic formula, so, would be necessary to find the inverse the matrix A...

 

[mfb]

If you don't find formulas, you can try the same approach as for normal matrices: solve analytically and write the final solution in matrix form again.
I'm not sure if that works here as your problem is not linear.