求帮忙算三个矩阵的最大特征值和特征向量,写论文急用,可是没有软件,第一个矩阵是161/61算最大特征值和特征向量第二个是1361/3121/61/21第三个是1421/411/21/221

Question

求帮忙算三个矩阵的最大特征值和特征向量,写论文急用,可是没有软件,
第一个矩阵是
1 6
1/6 1
算最大特征值和特征向量
第二个是
1 3 6
1/3 1 2
1/6 1/2 1
第三个是
1 4 2
1/4 1 1/2
1/2 2 1

Answer 1

以下内容中：v的对角线元素为特征值,d为对应的特征向量
>> A=[1,6;1/6,1]
A =
1.000000000000000 6.000000000000000
0.166666666666667 1.000000000000000
>> [d,v]=eig(A)
d =
0.986393923832144 -0.986393923832144
0.164398987305357 0.164398987305357
v =
2 0
0 0
>> B=[1,3,6;1/3,1,2;1/6,1/2,1]
B =
1.000000000000000 3.000000000000000 6.000000000000000
0.333333333333333 1.000000000000000 2.000000000000000
0.166666666666667 0.500000000000000 1.000000000000000
>> [d,v]=eig(B)
d =
-0.937042571331636 -0.975708253883806 0.738112692118793
-0.312347523777212 -0.081479780325272 -0.644578158472914
-0.156173761888606 0.203357932476604 0.199270297216658
v =
3.000000000000000 0 0
0 0.000000000000000 0
0 0 -0.000000000000000
>> C=[1,4,2;1/4,1,1/2;1/2,2,1]
C =
1.000000000000000 4.000000000000000 2.000000000000000
0.250000000000000 1.000000000000000 0.500000000000000
0.500000000000000 2.000000000000000 1.000000000000000
>> [d,v]=eig(C)
d =
-0.963086824686153 0.872871560943970 0
0.120385853085769 0.218217890235992 -0.447213595499958
0.240771706171538 0.436435780471985 0.894427190999916
v =
-0.000000000000000 0 0
0 3.000000000000000 0
0 0 0