Eigenvalues of a large Matrix

I have to plot the one of the eigenvalues of a large matirx in the following. The matrix is 20*20 dim. Numerically I have to get the eigenvalues and plot that. But the following code is not giving any plot. I have tried to plot it usnig ''For loop'' as normal plot is taking extremely huge time. But using '' for loop'' the plot is empty. Pl somebody help me to solve the long run time case here. Pl see below for my code.

clc;clear
syms x
a=1.0;
b=1.0;

n=20;

I1=eye(n);
I2=eye(2);
matdimension= (n-1);
tempvector = 0:1:matdimension;
tempvector = sqrt(tempvector);
tempmatrix = diag(tempvector);
crea= circshift(tempmatrix,-1);
anni = crea';

sc=(crea).^2;
sanni=(anni).^2;
num=crea*anni;
%creation = circshift(diag(sqrt(0:1:mat_dim)),-1)
sigx=[0,1;1,0];
sigz=[1,0;0,-1];

for x=0.0001:0.1:1.1    %% I need to plot u with x. But normally it is taking huge time as if never ending in the sysmbolic form of x. 
   f= a.*kron(num,I2) +(b./2).* kron(I1,sigz)+ x.*kron(sigx,(crea+anni)); 

    [~,v]=eig(f);
    u=v(1,1);
    plot(x,u,'r')
end

Answer 1

[KSSV]

clc; clear all ;
clc;clear

a=1.0;
b=1.0;

n=20;

I1=eye(n);
I2=eye(2);
matdimension= (n-1);
tempvector = 0:1:matdimension;
tempvector = sqrt(tempvector);
tempmatrix = diag(tempvector);
crea= circshift(tempmatrix,-1);
anni = crea';

sc=(crea).^2;
sanni=(anni).^2;
num=crea*anni;
%creation = circshift(diag(sqrt(0:1:mat_dim)),-1)
sigx=[0,1;1,0];
sigz=[1,0;0,-1];
figure
hold on
for x=0.0001:0.1:1.1    %% I need to plot u with x. But normally it is taking huge time as if never ending in the sysmbolic form of x. 
   f= a.*kron(num,I2) +(b./2).* kron(I1,sigz)+ x.*kron(sigx,(crea+anni)); 

    [~,v]=eig(f);
    u=v(1,1);
    plot(x,u,'*r')
end

OR

clc; clear all ;
clc;clear

a=1.0;
b=1.0;

n=20;

I1=eye(n);
I2=eye(2);
matdimension= (n-1);
tempvector = 0:1:matdimension;
tempvector = sqrt(tempvector);
tempmatrix = diag(tempvector);
crea= circshift(tempmatrix,-1);
anni = crea';

sc=(crea).^2;
sanni=(anni).^2;
num=crea*anni;
%creation = circshift(diag(sqrt(0:1:mat_dim)),-1)
sigx=[0,1;1,0];
sigz=[1,0;0,-1];

x=0.0001:0.1:1.1 ;
u = zeros(size(x)) ; 
for i = 1:length(x)    %% I need to plot u with x. But normally it is taking huge time as if never ending in the sysmbolic form of x. 
   f= a.*kron(num,I2) +(b./2).* kron(I1,sigz)+ x(i).*kron(sigx,(crea+anni)); 

    [~,v]=eig(f);
    u(i)=v(1,1);    
end
plot(x,u)

[AVM]

@Kssv: Thanks for your reply. It's working nicely. I would like to plot another two eigenvalues in same plot e.g. P(2,2) and Q(3,3). Is it possible to run inside the same '' for loop'? Pl help me.

[KSSV]

It should be.....you try out and see..if not post the code here. Thanks is acceptng the asnwer.

[AVM]

@KSSV: Why in your first example only star(*) or dot(.) in plot is vissible? No other style e.g. solid line or dashed line is not giving any graph.

[KSSV]

If you plot a single point...you should use a marker... ., ^ , etc,

[AVM]

Thanks for your information.