How to find and plot eigenvalues of symbolic 6*6 matrix

Question

I have a symbolic 6x6 matrics that I must find eigenvalues and plot them. I can't plot and I don't know what can I do.

    syms t H t1 t2 E1 E2 E3 E4 E5 E6 HH H1 v d H2 k a E;


t1=1;
t2=1.5*t1;
a=3;

H=[0 t2 0 0 0 t1  
    t2 0 t1 0 0 0
    0 t1 0 t2 0 0
    0 0 t2 0 t1 0
    0 0 0 t1 0 t2
    t1 0 0 0 t2 0];

H1=[0 0 0 0 0 0
    0 0 0 0 0 0
    0 0 0 0 0 0
    t1*exp(1i*k*a) 0 0 0 0 0
    0 0 0 0 0 0
    0 0 0 0 0 0];

H2=[0 0 0 t1*exp(1i*k*a) 0 0
    0 0 0 0 0 0
    0 0 0 0 0 0
    0 0 0 0 0 0
    0 0 0 0 0 0
    0 0 0 0 0 0];

HH=H+H1+H2;

E=eig (HH)

I can't run the [v,D]=eig(HH)
and I don't kno how to plot 6 different E(K) function

sorry for poor english and ppor knowledge of matlab and thanks for help!

Try to use the eigenvalue equation: det(HH - x.I) = 0, and solve *that*. — , May 15 '15 at 17:04

score 0 · Answer 1 · answered May 15 '15 at 17:21

I ran your code, and was able to do

[v,D]=eig(HH)

The diagonal values found in D will be your eigenvalues. Since you don't specify exact values for k, the output is too long to post here, but here is an example using only first matrix H:

syms t H t1 t2 E1 E2 E3 E4 E5 E6 HH H1 v d H2 k a E;


t1=1;
t2=1.5*t1;
a=3;

H=[0 t2 0 0 0 t1  
   t2 0 t1 0 0 0
   0 t1 0 t2 0 0
   0 0 t2 0 t1 0
   0 0 0 t1 0 t2
   t1 0 0 0 t2 0];

HH=H+H+H;

[v,D]=eig(HH)

Output:

v =

-0.4082   -0.2485   -0.5211    0.1548   -0.5562    0.4082
 0.4082    0.5290    0.2312   -0.2471   -0.5218    0.4082
-0.4082   -0.3271    0.4758   -0.5591    0.1441    0.4082
 0.4082   -0.0642   -0.5738   -0.3283    0.4749    0.4082
-0.4082    0.5756    0.0453    0.4043    0.4121    0.4082
 0.4082   -0.4648    0.3425    0.5754    0.0469    0.4082

D =

-7.5000         0         0         0         0         0
      0   -3.9686         0         0         0         0
      0         0   -3.9686         0         0         0
      0         0         0    3.9686         0         0
      0         0         0         0    3.9686         0
      0         0         0         0         0    7.5000

If you are trying to plot eigenvalues for varying values of k, my suggestion is to make a loop: Calculate the eigenvalues of HH for each value of k, and store these values into arrays. From there the plot should be pretty straightforward.

MATLAB documentation on plotting

How to find and plot eigenvalues of symbolic 6*6 matrix

1 Answers1