MATLAB: Eigenvalues of a large Matrix

eigenvalue

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

Best Answer

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)
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