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Inverse of a cubic matrix

  1. Apr 10, 2015 #1
    Be the matrix A defined by [aijk] (a matrix 2x2x2), do you know how to compute a inverse this cubic matrix?
  2. jcsd
  3. Apr 10, 2015 #2


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    First you would need to define what you mean by the inverse of a cubic matrix.
  4. Apr 10, 2015 #3


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    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.
  5. Apr 18, 2015 #4
    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...
  6. Apr 18, 2015 #5


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    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.
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