二次型f(x1,x2,x3)=(x1-x2)^2+(x2-x3)^2的矩阵是什么,怎么求?
问题描述:
二次型f(x1,x2,x3)=(x1-x2)^2+(x2-x3)^2的矩阵是什么,怎么求?
答
[x1 x2 x3][1 -1 0 ; -1 2 -1 ; 0 -1 1][x1 x2 x3]T
答
f(x1,x2,x3)=(x1-x2)^2+(x2-x3)^2
=x1^2 - 2x1x2 + 2x2^2 - 2x2x3 + x3^2
A =
1 -1 0
-1 2 -1
0 -1 1