Nearest block diagonal matrix to a given matrix

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The discussion centers on finding the nearest block diagonal matrix to a given matrix, specifically in terms of the Frobenius norm. The problem is relevant to quantum chemistry research, where such matrix transformations are necessary. The original poster initially sought assistance but later resolved the issue independently after a week of contemplation. The uniqueness of the block diagonal form, defined by unitary rotations, is acknowledged as a key consideration. The conversation highlights the challenges and eventual self-solution in mathematical matrix transformations.
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Suppose I have a matrix that I want to reduce to block diagonal form. Obviously, the block diagonal form is not unique as each of the diagonal blocks is defined only to within a unitary rotation. So I want to find the block diagonal matrix that is closest to the original matrix in terms of the Frobenius norm.

This problem arises in a quantum chemistry manuscript I am putting together. If anyone can point me to a solution for this, I would be more than happy to acknowledge them in the manuscript.

Thanks!
 
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Okay, I figured it out myself. After thinking about it for a week, I solve it right after posting!
 

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