MATLAB: Eigenvalues corresponds to eigenvectors

Question

In matlab, the command [V,L]=eig(h) produces the eigenvectors and eigenvalues of the square matirx h. But I would like to know in which order this eigenvectors appear? I mean how can I observe that which eigenvalues corresponds to which eigenvectors. I am really confused at this point. Pl somebody help me to understand this. Here I have taken an example.

clc;clear;
syms a b c
h=[a 0 1 0;0 b 2 0;1 0 c 0;0 3 0 a];
[V,L]=eig(h)

This produces the output as

 
V =
 
[ 0,         0,                                a/12 - b/6 + c/12 - (a^2 - 2*a*c + c^2 + 4)^(1/2)/12,                                a/12 - b/6 + c/12 + (a^2 - 2*a*c + c^2 + 4)^(1/2)/12]
[ 0, b/3 - a/3,                                         c/6 - a/6 - (a^2 - 2*a*c + c^2 + 4)^(1/2)/6,                                         c/6 - a/6 + (a^2 - 2*a*c + c^2 + 4)^(1/2)/6]
[ 0,         0, (a*b)/6 - (a*c)/6 - (b/6 - c/6)*(a/2 + c/2 - (a^2 - 2*a*c + c^2 + 4)^(1/2)/2) + 1/6, (a*b)/6 - (a*c)/6 - (b/6 - c/6)*(a/2 + c/2 + (a^2 - 2*a*c + c^2 + 4)^(1/2)/2) + 1/6]
[ 1,         1,                                                                                   1,                                                                                   1]
 
 
L =
 
[ a, 0,                                           0,                                           0]
[ 0, b,                                           0,                                           0]
[ 0, 0, a/2 + c/2 - (a^2 - 2*a*c + c^2 + 4)^(1/2)/2,                                           0]
[ 0, 0,                                           0, a/2 + c/2 + (a^2 - 2*a*c + c^2 + 4)^(1/2)/2]
 

But how do I associate the eigenvector with its corresponding eigenvealue.

Answer 1

Absolutely standard: L(k,k) ~ V(:,k).

You can check it with the code:

for k=1:size(h,1)
disp(strcat('k=',num2str(k),'; h*v-lambda*v=',num2str(double(norm(simplify(h*V(:,k) - L(k,k)*V(:,k)))))));
end