I'm not exactly sure about the context of your question, but those vectors are independent.
Don't know if that helps or not.
Hi all, I have been asked to diagonalize the matrix [-1,3 ; 3,2] and I am supposed to notice something special about the eigenvectors.
Eigenvectors are as follows:
[-1.61803 ; 1] and [.61803 ; 1]. They are independent etc....not sure what is so special about them...
it might help if you wrote the ACTUAL values for the eigenvectors, and not just decimal approximations (decimals are BAD! unless you're a physicist. silly them).
i get as eigenvalues:
leading to the following eigenvectors:
in other words, the eigenvectors are ORTHOGONAL.