It is known that when $\mathbf{A}$ is real, symmetric and positive definite, all its eigenvalues are real positive (tell me if I'm wrong, though).
Looking for a similar condition for generalized eigenvalue porblems: \begin{align} \mathbf{Ax} = \lambda\mathbf{Bx} \end{align}
where both matrices are real and symmetric, and $\mathbf{B}$ is positive definit. So far I found that in this case all eigenvalues a real. However I would need a condition for the positivity as well. So the question is:
Is there a condition for matrices $\mathbf{A}$ and $\mathbf{B}$ so that all $\lambda$ values are real and positive?