linear algebra - Can a positive definite matrix have complex eigenvalues?

We know that a positive definite matrix has positive eigenvalues. I wanted to know if there is any result that shows whether a positive definite matrix can have complex eigenvalues.
I am currently calculating a covariance matrix which has real entries and is symmetric. In order to find the accuracy of the calculation, I tried to find the eigenvalues of the matrix and then generate c-code using MATLAB coder to use in my Kalman filter equations. However, when the coder gives error that the eigenvalues are complex. It is to be noted that the first two eigenvalues of the matrix are close two zero.