>>  A=[16 2 3 13; 5 11 10 8; 9 7 6 12; 4 14 15 1]; eig(A), [v,d]=eig(A)

ans =

   34.0000
    8.9443
   -8.9443
   -0.0000


v =

   -0.5000   -0.8236    0.3764   -0.2236
   -0.5000    0.4236    0.0236   -0.6708
   -0.5000    0.0236    0.4236    0.6708
   -0.5000    0.3764   -0.8236    0.2236


d =

   34.0000         0         0         0
         0    8.9443         0         0
         0         0   -8.9443         0
         0         0         0   -0.0000

v为特征值对应的特征向量

>> eig(sym(A)),vpa(ans,30),[v,d]=eig(sym(A))
 
ans =
 
         0
        34
-4*5^(1/2)
 4*5^(1/2)
 
 
ans =
 
                               0
                            34.0
-8.94427190999915878563669467493
 8.94427190999915878563669467493
 
 
v =
 
[-1, 1, (12*5^(1/2))/31 - 41/31, - (12*5^(1/2))/31 - 41/31]
[-3, 1,  17/31 - (8*5^(1/2))/31,    (8*5^(1/2))/31 + 17/31]
[ 3, 1, - (4*5^(1/2))/31 - 7/31,     (4*5^(1/2))/31 - 7/31]
[ 1, 1,                       1,                         1]
 
 
d =
 
[0,  0,          0,         0]
[0, 34,          0,         0]
[0,  0, -4*5^(1/2),         0]
[0,  0,          0, 4*5^(1/2)]

 变换成对角矩阵

 >> syms c1 c2 c3 real;H=compan([1 c1 c2 c3]);[V,D]=eig(H)   先构造相伴矩阵

>>  B=[2,6,-1,-2; 5,-1,2,3; -3,-4,1,10; 5,-2,-3,8]; A=[5,7,6,5; 7,10,8,7; 6,8,10,9; 5,7,9,10]; [V,D]=eig(A,B)

V =

   0.3697 + 0.0000i  -0.3741 + 0.6259i  -0.3741 - 0.6259i   1.0000 + 0.0000i
   0.9948 + 0.0000i  -0.0674 - 0.2531i  -0.0674 + 0.2531i  -0.6090 + 0.0000i
   0.7979 + 0.0000i   0.9239 + 0.0264i   0.9239 - 0.0264i  -0.2316 + 0.0000i
   1.0000 + 0.0000i  -0.6599 - 0.3263i  -0.6599 + 0.3263i   0.1319 + 0.0000i


D =

   4.7564 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0471 + 0.1750i   0.0000 + 0.0000i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0471 - 0.1750i   0.0000 + 0.0000i
   0.0000 + 0.0000i   0.0000 + 0.0000i   0.0000 + 0.0000i  -0.0037 + 0.0000i

>>  norm(A*V-B*V*D)

ans =

   3.3761e-14