Positive Definite Matrices and eigenvalues Problem:

Let $A$ ∈ ${C}^{n×n}$ be, such that for every x ∈ $C^n$ <$A$x$, x$> ≥ 0
Show that all eigenvalues of $A$ are positive or zero

I suppose that from the standart inner product in the problem we can say that $A$ is a positive definite matrix and therefore follows that the eigenvalues of $A$ are positive.
However I am not sure if that is right,could someone give a hint?

It's a straightforward computation. If $\lambda$ is an eigenvalue of $A$, choose an eigenvector $v$ with $\langle v,v\rangle=1$. Then 
$$
\lambda=\langle \lambda v,v\rangle=\langle Av,v\rangle\geq0. 
$$
