f(x1, x2,",xn)=a11x1+a12x1x2+a13x1x3+.+aNxin +a21x2X1+a22x2+423x2x3+…+a2nx2xn 2 tanXnxtanXnx2tanxnx3+.tannan auIX1+anx 12 2 ∴ nn 21x1+a22x2+…+a2nXn 1n1x1+an2x2+…+amxn x =(x1,x 2n 2 2 x 72 =XAX二次型的矩阵表示式n n n f x x x a x a x x a x x a x x 12 1 2 13 1 3 1 1 2 1 2 11 1 ( , ,  , ) = + + ++ n n a x x a x a x x a x x 23 2 3 2 2 2 + 21 2 1 + 22 2 + ++ 2 n1 n 1 n2 n 2 n3 n 3 nn n + a x x + a x x + a x x ++ a x +               n x x x  2 1               n n nn n n a a a a a a a a a        1 2 21 22 2 11 12 1 ( , , , ) 1 2 n = x x  x               + + + + + + + + + n n nn n n n n n a x a x a x a x a x a x a x a x a x     1 1 2 2 21 1 22 2 2 11 1 12 2 1 ( , , , ) 1 2 n = x x  x X AX T = 二次型的矩阵表示式