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85问答库 > 用配方法将二次型f ( x1 x2 x3 ) = x1^2-X2X3化为标准型怎么做呢？

用配方法将二次型f ( x1 x2 x3 ) = x1^2-X2X3化为标准型怎么做呢？

2025-02-18 18:24:48

推荐回答（1个）

回答1：

观察有x2 x3 而x2 x3 并没有平方项

那么令x1=y1.x2=y2+y3 x3=y2-y3

那么就变成了y1^2-y2^2+y3^2=0

所用变换 C= （1 0 0
0 1 1
0 1 -1 ） |C|不等于0 这个变换成立

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