A=[5 9 9;-72 -79 -72; 90 90 80];
[V,lambda]=eig(A);
cond(V)

B=[5 9.1 9;-72 -79 -72; 90 90 80];
C=[5 9 9;-72 -78.9 -72; 90 90 80];
F=[5 9 9;-72 -79 -72; 89.9 90 80];
mu=[eig(A) eig(B) eig(C) eig(F)]

A=[2 -1 4; -1 1 -3; 4 -3 5];
[V,lambda]=eig(A);
cond(V)

B=[2.1 -1 4; -1 1 -3; 4 -3 5];
C=[2 -1 4; -1 0.9 -3; 4 -3 5];
F=[2 -1 4; -1 1 -3; 3.9 -3 5];
mu=[eig(A) eig(B) eig(C) eig(F)]

A=[5 9 9;-72 -79 -72; 90 90 80];
[V,lambda]=eig(A); [Y,mu]=eig(A');
c_eig=[norm(Y(:,1))*norm(V(:,1))/abs(Y(:,1)'*V(:,1)), ...
        norm(Y(:,2))*norm(V(:,2))/abs(Y(:,2)'*V(:,2)), ...
        norm(Y(:,3))*norm(V(:,3))/abs(Y(:,3)'*V(:,3))]'

condeig(A)

B=[5 9.1 9;-72 -79 -72; 90 90 80];
C=[5 9 9;-72 -78.9 -72; 90 90 80];
F=[5 9 9;-72 -79 -72; 89.9 90 80];
Delta=[abs(eig(B)-eig(A)) abs(eig(C)-eig(A)) abs(eig(F)-eig(A))]

A=[2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0; ...
     0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0; 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0; ...   
     0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0; 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0; ... 
     0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0; 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0; ... 
     0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0; 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0; ... 
     0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0; 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0; ... 
     0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0; 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0; ...
     0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1; 10^-16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2];
lambda=eig(A);
plot(real(lambda),imag(lambda),'dr'); hold on;
t=[0:0.01:2*pi];
plot(2+0.1*sin(t),0.1*cos(t),'--'); 
axis([1.85 2.15 -.15 .15]);