Solving a PDE Eigenvalue Problem: Proving All Eigenvalues Are Positive

[ekalbh]

I have a PDE test next week and I'm kinda confused. How do you prove that eigenvalues are all positive? I know Rayleigh Quotient shows the eigenvalues are greater than or equal to zero, but can someone explain the next step. Thanks in advance

 

[Feldoh]

All eigenvalues are not positive. Are you talking about the eigenvalues of Hermitian operators?

 

[ekalbh]

Sorry, I mean given a pde, how would you go about finding out if the eigenvalues are positive, negative, zero, or a combination of those.