Proof:Suppose A is a reel skew-symmetric matrix,and λ is a eigenvalue of A. That is,Aα=λα (α=(a1,a2,...,an)') we multply by (α共轭)’on both sides (α共轭)'Aα=(α共轭)'λα=λ(α共轭)'α on the other hand (α共轭)'Aα=(α共轭)'(-A')α=-(Aα的共轭)'α=-(λα共轭)'α so λ(α共轭)'α=-(λα共轭)'α=-λ(α共轭)'α so λ=-λ we suppose λ=a+bi that is a=0 λ=0 or λ=bi