证明：S=I-2XX^TS^T=(I-2XX^T)^T=I^T-2(XX^T)^T=I-2XX^T∴S=S^T，即S是对称矩阵。S^2=(I-2XX^T)(I-2XX^T)=I-2XX^T-2XX^T+4(XX^T)(XX^T)=I-4XX^T+4X(X^TX)X^T=I-4XX^T+4XX^T=IS^2=I
