I have encountered the fact on wikipedia that every skew-symmetric matrix can be block-diagonalized, where the matrix is in the form indicated by the following picture. I was wondering if there is a proof for such a statement through diagonalizing $M^2$, since $M^2$ is self-adjoint and can be diagonalized into orthonormal basis by spectral theorem.
2026-03-26 04:51:18.1774500678
How to block-diagonalize a skew symmetric matrix
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