# Real skew symmetric matrix block-diagonal form

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

• Do you know about complex Hermitian matrices? Do you know about the spectral theorem? – Omnomnomnom Aug 8 '16 at 20:12
• @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). – GregVoit Aug 9 '16 at 4:57
• 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. – Omnomnomnom Aug 9 '16 at 5:10
• @Omnomnomnom yes. Could you maybe provide a reference where I can see the proof? Thank you – GregVoit Aug 9 '16 at 5:24