Fast eigen decomposition algorithm for Skew Symmetric matrix

Question

The symmetric Matrix's eigen decomposition has fast algorithm, I wonder whether there is on for skew symmtric matrix.

I assume this question is dual to symmtric matrix eigen prob. Because all symmetric matrix's eigenvalues are real, while all skew symmetric matrix's eigenvalues are imag.

If there is existing algorithm and lib code, it would be appreciated too.

Thank you.

Answer 1

If $A$ is skew-Hermitian (in particular, if it is real and skew-symmetric) then $iA$ is Hermitian. Use a Hermitian eigenvalue routine on $iA$ (e.g. LAPACK's cheev) and divide the eigenvalues you get by $i$.