Eigenvalues of a skew symmetric matrix

The eigenvalues of a real skew symmetric matrix can be zero or imaginary. I figured out that they can be zero but i can't figure out, how can they be imaginary ? I don't know why, the idea doesn't seem to fit in my head even though it is true.

If someone could explain this to me it would be a great help.

Thanks in advance.

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Re: Eigenvalues of a skew symmetric matrix

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**mrmaaza123** The eigenvalues of a real skew symmetric matrix can be zero or imaginary. I figured out that they can be zero but i can't figure out, how can they be imaginary ? I don't know why, the idea doesn't seem to fit in my head even though it is true.

If someone could explain this to me it would be a great help.

Thanks in advance.

I think there's a good proof of this in page 6-14 of this document(btw, this lecture note is great (Talking))