命题3f(α,β)为V上反对称双线性函数台 对 VαV f(α,α)=0.证: "→"f(α,α)=-f(α,α)= f(α,α)=0. αV"←"f(α+β,α+β)= f(α,β)+ f(β,α)+ f(α,α)+ f(β,β)= f(α,β)+ f(β,α)= 0= f(α,β)=-f(β,α)810.4对称双线性函数§10.4 对称双线性函数 命题3 f ( , )   为V上反对称双线性函数 " " ( , ) ( , ) ( , ) 0.  = −  =   f f f V        " " ( , )  + + f      + = f f ( , ) ( , ) 0     证:  对   =    V f ( , ) 0. = + + + f f f f ( , ) ( , ) ( , ) ( , )          = − f f ( , ) ( , )    