用MATLAB求矩阵特征值.docx

用matlab求矩阵的特征值和特征向量
我要计算的矩阵:
1 3 5
1/3 1 3
1/5 1/3 1
[v,d]=eig(A);
A为你的矩阵,V为特征向量矩阵,D为特征值矩阵,然后对D求最大值即可得最大特征根!
[V,D] = EIG(X) produces a diagonal matrix D of eigenvalues and a full matrix V whose columns are the corresponding eigenvectors so that X*V = V*D.
V是特征向量,D是特征值
实例:
矩阵:
1 2/3 7/3 7/3
3/2 1 3/2 3/2
3/7 2/3 1 3/2
3/7 2/3 2/3 1
>> format rat
>> A=[1 2/3 7/3 7/3
3/2 1 3/2 3/2
3/7 2/3 1 3/2
3/7 2/3 2/3 1]
A =
1 2/3 7/3 7/3
3/2 1 3/2 3/2
3/7 2/3 1 3/2
3/7 2/3 2/3 1
>> [V,D]=eig(A)
V =
1793/2855 504/3235 - 146/235i 504/3235 + 146/235i 1990/4773
670/1079 -3527/5220 -3527/5220 -509/959
4350/11989 1160/4499 + 287/3868i 1160/4499 - 287/3868i -350/647
838/2819 181/3874 + 1179/4852i 181/3874 - 1179/4852i 1238/2467
D =
810/197 0 0 0
0 -93/4229 + 455/674i 0 0
0 0 -93/4229 - 455/674i 0
0 0 0 -149/2201
*****************************************************************************************
如何归一化求权重呢?
>> a=[1 3 5;1/3 1 3; 1/5 1/3 1]
a =



>> [V,D]=eig(a)
V =

- + - -
- - - +
D =
0 0
0 - + 0
0 0 - -
**************************************************************************
>> a=[1 2 4 8 6 6 8;1/2 1 2 6 4 4 8;1/4 1/2 1 4 2 4 6;