Eigenvalues of Real Skew-Symmetric Matrix are Zero or Purely Imaginary and the Rank is Even
Problem 269
Let $A$ be a real skew-symmetric matrix, that is, $A^{\trans}=-A$.
Then prove the following statements.
(a) Each eigenvalue of the real skew-symmetric matrix $A$ is either $0$ or a purely imaginary number.
(b) The rank of $A$ is even.
Add to solve later