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I have a 3-dimensional array that is potentially very large and I need to do quite a lot of operations with it.

Is there a systematic way to choose a subspace of a certain size, such that the norm (any norm) of the projection of the array onto the subspace is as large as possible?

If it was two dimensions I would diagonalize and then then add eigenvectors to my subspace with the largest eigenvalue until I was satisfied. But what do you do with 3-dimensional array?

Btw, I'm a physicist and the 3-dimensional array is the electron-phonon coupling:)

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