Can eigenvalues of a correlation matrix be negative?
I am a bit confused because I know that a correlatin matrix $C$ is always positive semi-definite ie for all $v \in \mathbb R^n$ we have $v^T C v \geq 0$. Doesn't it implies that for all eigenvalues $\lambda_i$of $C$ with $i = 1, \cdots, n$ we have tha $\lambda_i \geq$ 0?