## 每週問題 January 30, 2017

Prove that the rank of a real skew-symmetric matrix is an even number.

$\overline{\lambda}\mathbf{x}^\ast\mathbf{x}=(\lambda\mathbf{x})^\ast\mathbf{x}=(A\mathbf{x})^\ast\mathbf{x}=\mathbf{x}^\ast A^T\mathbf{x}=-\mathbf{x}^\ast A\mathbf{x}=-\lambda\mathbf{x}^\ast\mathbf{x}$