How to diagonalize NxNxNxN matrix

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Diagonalizing an NxNxNxN symmetric matrix involves understanding its structure as a tensor rather than a traditional matrix. The discussion highlights the confusion around defining such a matrix and emphasizes that it consists of four indices (ijkl). It also notes that existing BLAS routines are not applicable for this higher-dimensional case. The conversation suggests that the problem may require tensor operations rather than standard matrix techniques. Understanding the tensor rank and how to manipulate these higher-dimensional objects is crucial for finding eigenvalues and eigenvectors.
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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.
 
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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?
 
I misspoke, it's not a 4D matrix, it's an N by N by N by N matrix. So there are ijkl indices.
 
In what sense would you multiply two NxNxNxN objects?
 
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.
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

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