0
$\begingroup$

If $A$ is a real symmetric matrix, can I prove that all of the eigenvalues of $A$ are real and that all eigenvectors associated with distinct eigenvalues are orthogonal? If so, where do I start to prove that?

$\endgroup$
0
$\begingroup$

Yes, this is a famous result known as the "spectral theorem". It's a little easier to prove over the complex numbers, but the real symmetric case isn't that much harder. See http://en.wikipedia.org/wiki/Spectral_theorem#Hermitian_maps_and_Hermitian_matrices .

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.