I am looking for an automated method for the diagonalization of multidimensional matrices (Cubic 3D matrices, for example). Any suggestion would be much appreciated.
I'm not sure if it will work in more than 3 dimensions, but in 3 it seems like you can diagonalize 2D matrices along one axis. You end up with a 2D matrix diagonally across the "volume" of the original matrix. You can then diagonals this matrix. Keeping track of all the transformations would an issue if you need to do anything with that information.