令X=(x1,x2,…x),则二次型的矩阵形式为 f(x,x…x)=XAX∑ a=a 12 22 3 =(x,x2,…,x)a31a32a3…an n3 nn令 ( , , , ) , T 1 2 n X = x x  x 则二次型的矩阵形式为 f (x1 , x2 , xn ) = X A X T ( , , , ) 1 2 n = x x  x                 n n n n n n n n a a a a a a a a a a a a a a a a          1 2 3 3 1 3 2 3 3 3 2 1 2 2 2 3 2 1 1 1 2 1 3 1             n x x x  2 1 ( ) , 1 i j j i n i j i j i j =a x x a = a =