n=5
A=rand(n,n)
A=A'*A
v=rand(n,1)
for k=[1:20] 
    v=A*v
    pause(0.5)
end
[V,D]=eig(A)
pause

myfig=clf
hold on
A=2*rand(n,n)-1;
A=A'*A
v=2*rand(n,1)-1
for k=[1:20] 
    v=A*v;
    v=v/sqrt(v'*v) 
    plot(v)
    figure(myfig)
    pause(1)
end
[V,D]=eig(A)
pause


n=2
myfig=clf
hold on
axis([0 3 -1 2])
A=2*rand(n,n)-1;
A=A'*A
v=2*rand(n,1)-1
v=v/sqrt(v'*v);
for k=[1:20]
    plot(v)
    figure(myfig)
    v=A*v
    v=v/sqrt(v'*v) 
    pause(1)
end
[V,D]=eig(A)
pause

n=2
myfig=clf
axis([-1 1 -1 1])
hold on
A=2*rand(n,n)-1;
A=A'*A
v=2*rand(n,1)-1
v=v/sqrt(v'*v)
for k=[1:20]
    plot([0,v(1)],[0,v(2)])
    figure(myfig)
    v=A*v;
    v=v/sqrt(v'*v) 
    pause(1) 
end
[V,D]=eig(A)
pause

%% cool examples

n=2
myfig=clf
axis([-1 1 -1 1])
hold on
A =[ 0.582246391421335   0.340007729787364;...
     0.629904135866459  -0.598247175409675]
v=2*rand(n,1)-1
v=v/sqrt(v'*v)
for k=[1:20]
    plot([0,v(1)],[0,v(2)])
    figure(myfig)
    v=A*v;
    v=v/sqrt(v'*v) 
    pause(1) 
end
[V,D]=eig(A)
pause

n=2
myfig=clf
axis([-1 1 -1 1])
hold on
A =[0.073703389635012  -0.822076481049350;...
   -0.880991898159001  -0.457383651236600]
v=2*rand(n,1)-1
v=v/sqrt(v'*v)
for k=[1:20]
    plot([0,v(1)],[0,v(2)])
    figure(myfig)
    v=A*v;
    v=v/sqrt(v'*v) 
    pause(1) 
end
[V,D]=eig(A)
pause