# Can a Covariance matrix have negative elements?

I have a $N \times N$ covariance matrix $C$ of a multivariate Normal distribution. Can any of the elements of the Covariance matrix $C$ be negative for a real-valued distributions ?

Yes, for example $$\begin{pmatrix} a+b & a-b \\ a-b & a+b \end{pmatrix}$$ can appear as covariance matrix for any positive eigenvalues $2a$, $2b$.