Question

求非退化线性替换

求非退化线性替换，把二次型f(x1,x2,x3)=2x1x2+2x2x3化为标准形

Answer 1

解: 令 x1=y1+y2, x2=y1-y2, x3=y3, 则
f = 2y1^2-2y2^2+2y1y3-2y2y3
= 2(y1+(1/2)y3)^2-2(y2+(1/2)y3)^2
= 2u^2-2v^2
u=y1+(1/2)y3
v=y2+(1/2)y3
w=y3
得
x1=u+v-w
x2=u-v
x3=w

满意请采纳^_^

Answer 2

f = 2u^2-2v^2