true or false: eigenvectors of a 2 x 2 matrix are always perpendicular to each other? in matlab

To determine whether eigenvectors of a 2 x 2 matrix are always perpendicular to each other, you can use the dot product between the eigenvectors.

In MATLAB, given a matrix A, you can find the eigenvectors using eig function:

main.m
A = [a, b; c, d]; % replace with your matrix entries
[eigenvecs, ~] = eig(A);
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To determine if the eigenvectors are perpendicular, calculate the dot product between them and check if the result is close to zero (assuming floating-point precision):

main.m
dot_result = dot(eigenvecs(:,1), eigenvecs(:,2));
is_perpendicular = abs(dot_result) < 1e-6; % adjust the tolerance as needed
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The variable is_perpendicular will be true if the eigenvectors are perpendicular, and false otherwise.

Remember that due to numerical calculations, the dot product might not be exactly zero, so using a tolerance is recommended.