求下列实对称矩阵A,求一个正交矩阵P,使P^-1AP=P^TAP=D为对角矩阵
1 2 2
2 1 2
2 2 1
人气:284 ℃ 时间:2019-10-23 06:19:44
解答
|A-λE| = (5-λ)(1+λ)^2.
所以A的特征值为 5,-1,-1
(A-5E)X = 0 的基础解系为:a1 = (1,1,1)'
(A+E)X = 0 的基础解系为:a2 = (1,-1,0)',a3 = (1,0,-1)'
将 a2,a3 正交化得 b2 = (1,-1,0)',b3 = (1/2,1/2,-1)'
单位化得
c1 = (1/√3,1/√3,1/√3)',
c2 = (1/√2,-1/√2,0)',
c3 = (1/√6,1/√6,-2/√6)'
令矩阵P = (c1,c2,c3),则P为正交矩阵,且 P^-1AP = diag(5,-1,-1).
推荐
- 对下列实对称矩阵A,求一个正交矩阵P,使P^-1AP=P^TAP=D为对角矩阵 2 0 0 0 -1 3 0 3 -1
- 对下列实对称矩阵A,求一个正交矩阵P,使P^-1AP=P^TAP=D为对角矩阵(9 -2 ,-2 9)
- 对下列实对称矩阵A,求一个正交矩阵P,使P^-1AP=P^TAP=D为对角矩阵 【1,2,2;2,1,2;2,2,1】
- 请在这里概述您的问题对下列实对称矩阵A,求一个正交矩阵P,使P^-1AP=P^TAP=D为对角矩阵 2 1 0 1 3 1 0 1
- 请在这里概述您的问题对下列实对称矩阵A,求一个正交矩阵P,使P^-1AP=P^TAP=D为对角矩阵 [9,-2;-2,6]
- That man knows a lot about New York.I heard he ()before
- 两根长度相同的圆轴,受相同的扭矩作用,
- 速度为每小时50千米的船只如果能绕地球赤道一周的话,大概需要航行
猜你喜欢