See this dialog response. From the spectral theorem, for a real skew-symmetric matrix the nonzero eigenvalues are all pure imaginary and thus are of the form formula_73 where each of the formula_74 are real. What came before?
DIALOG:
 * what does the following result mean?.
 * this elucidates the relation between three-space formula_72, the cross product and three-dimensional rotations..
 * Are there any other interesting aspects about this article?.
 * More on infinitesimal rotations can be found below..
 * what about the transpose of the matrix?.
 * Since a matrix is similar to its own transpose, they must have the same eigenvalues..
 * does the matrix have any other meanings?.
 * It follows that the eigenvalues of a skew-symmetric matrix always come in pairs ±λ (except in the odd-dimensional case where there is an additional unpaired 0 eigenvalue)..
 * what about the eigenvalues?.
 * 