Matlab suddenly changes from positive values to negative values when calculating eigenvectors/plotting a graph (a bug?)

Question

I have written the following piece of code with your help:

M = [3  0  0.0; 
     0  2  0.0; 
     0  0  0.5];   % mass matrix

i_vals = 0:1000:60e06;   % values of k_12 from 1 to 600 million in steps of 1000
modes = zeros(3, length(i_vals));

for n=1:length(i_vals)
    i = i_vals(n);    % i is the value of k_12
    K = [i+8e06 -i -2e06; -i i+2e06 -1e06; -2e06 -1e06 5e06];    % stiffness matrix

    [V,L]=eig(K,M);         

    modes(:, n) = V(:,1); % natural frequency can be either 1, 2 or 3

end

semilogx(i_vals, modes')
    title('Effect of change of value of k_1_2 on the value of mode shapes for the first natural frequency');
    xlabel('Value of k_1_2 [N/m]');
    ylabel('Value of mode shapes]');
    hleg1 = legend('mode shape 1','mode shape 2', 'mode shape 3');
    grid on;
    grid minor;

The problem is at some values Matlab suddenly switches from positive to negative values:

Is this due to the eig()function or not? How is that possible to fix it?

Answer 1

Eigen-vectors are always determined up to a sign, since multiplying an eigenvector by -1 does not change its status as an eigenvector. You can try using eigenshuffle from the FEX .