Linear Algebra 22d: Symmetric Matrices (Even with Repeated Eigenvalues) Have Orthogonal Eigenvectors

[enriqueesparza]

Thanks a lot. I got confused in lecture when my teacher said you can always "choose" the eigenvectors to be perpendicular. This really cleared it up. :)

[UnknownCynogale]

so does it means that if we have two eigenvectors corresponding to an eigenvalue, we can change the eigenvector to make it orthogonal? how do we know which one of these two eigenvectors we should change? is it completely up to us? thanks