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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.

Vladimir Sovkov
on 8 Feb 2020

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

Vladimir Sovkov
on 9 Feb 2020

The array indexing is described at https://www.mathworks.com/help/matlab/math/array-indexing.html?searchHighlight=matrix%20indexing&s_tid=doc_srchtitle

E.g., you address the entire k-th column of a matrix as V(:,k).

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