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I am looking for a proof (preferably available online) of the statement that every real skew symmetric matrix can be brought into block diagonal form, with blocks formed by the pure imaginary eigenvalues.

I have often come across this statement but it always seems to be taken as a known fact. I would like to see a complete proof.

Thank you

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  • $\begingroup$ Do you know about complex Hermitian matrices? Do you know about the spectral theorem? $\endgroup$ – Omnomnomnom Aug 8 '16 at 20:12
  • $\begingroup$ @Omnomnomnom if I'm not mistaken, those are for diagnoalization. What I need is block-diagonal, with eigenvalues in blocks (not 1's or -1's). $\endgroup$ – GregVoit Aug 9 '16 at 4:57
  • $\begingroup$ That's right, but we can use diagonalization as a stepping stone. Also, I have no idea what "not 1's or -1's" is supposed to mean here. I assume you're talking about finding a block diagonal matrix similar to your skew-symmetric matrix. $\endgroup$ – Omnomnomnom Aug 9 '16 at 5:10
  • $\begingroup$ @Omnomnomnom yes. Could you maybe provide a reference where I can see the proof? Thank you $\endgroup$ – GregVoit Aug 9 '16 at 5:24

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