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How to diagonalize NxNxNxN matrix

  1. Jul 8, 2008 #1
    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.

  2. jcsd
  3. Jul 8, 2008 #2


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    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?
  4. Jul 8, 2008 #3
    I misspoke, it's not a 4D matrix, it's an N by N by N by N matrix. So there are ijkl indices.
  5. Jul 8, 2008 #4
    In what sense would you multiply two NxNxNxN objects?
  6. Jul 9, 2008 #5
    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.
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