How to diagonalize NxNxNxN matrix

[ann3]

I have a symmetric NxNxNxN matrix that I need to find eigenvalues a eigenvectors for. All the BLAS routines are for NxN matrices and I can't find anything that would work on a 4D matrix. Any tricks you guys know of?
If it helps to know, it's a Hamiltonian and I want to find energies and wavenfunctions.

Thanks.

 

[HallsofIvy]

First of all, how are you going to define an "NxNxNxN" matrix? A "4D matrix" is just a 4x 4 matrix. On what space is such a matrix acting?

 

[ann3]

I misspoke, it's not a 4D matrix, it's an N by N by N by N matrix. So there are ijkl indices.

 

[maze]

In what sense would you multiply two NxNxNxN objects?

 

[WarPhalange]

I think you're talking about Tensors now. Rank 0 tensor = Scalar, rank 1 tensor = vector, rank 2 tensor = matrix, rank 3+ is where you get into stuff you can't really visualize.