线性代数,求特征值,将二次型化为标准型,求大神过程,要考试

2025-01-19 14:10:57
推荐回答(1个)
回答1:

|λE-A| =

|λ-1 0 0 1|
|0 λ-1 0 0|
|0 0 λ+1 0|
|1 0 0 0|
|λE-A| = (λ-1)(λ+1)*
|λ-1 1|
|1 0|
= -(λ-1)(λ+1) = 0
特征值 λ = 1, λ = -1
f = (x1-x4)^2+(x2)^2-(x3)^2-(x4)^2
= (y1)^2+(y2)^2-(y3)^2-(y4)^2