f(α,β)= f(β,α)α X'AY =Y'AX=(Y'AX)'= X'A'Y f(8),8,)= f(6j,6)aj =ajiA=A.同样 f(α,β)=-f(β,α)≤ f(8;,8,)=-f(8,8,)台X'AY=-Y'AX=-X'A'Y←A=-AS10.4对称双线性函数K§10.4 对称双线性函数 f f X AY Y AX ( , ) ( , ) ' '     =  = ( , ) ( , ) i j j i  = f f     = = ( ' )' ' ' Y AX X A Y 同样 ( , ) ( , ) ( , ) ( , ) i j j i f f f f         = −  = −  = − = − X AY Y AX X A Y ' ' ' '  = A A'. ij ji  = a a  = − A A