线性代数二次型配方法

2025-05-13 12:41:03
推荐回答(1个)
回答1:

将 x1 = y1 + y2, x2 = y1 - y2 , x3 = y3 代入 f = 2x1x2 + 2x1x3 - 6x2x3, 得
f = 2(y1)^2 - 2(y2)^2 + 2(y1+y2)y3 - 6(y1-y2)y3
= 2(y1)^2 - 2(y2)^2 + 2y1y3 + 2y2y3 - 6y1y3 + 6y2y3
= 2(y1)^2 - 2(y2)^2 - 4y1y3 + 8y2y3