I am learning that operators corresponding to observable quantities are Hermitian since the eigenvalues are real. This makes sense (at least intuitively) and I have seen corresponding proofs of why eigenvalues of Hermitian operators are always real. That is fine. But are there any other types of operators (i.e. non-Hermitian) that correspond to observable quantities? Are not Hermitian operators only one such type of matrix that can produce real eigenvalues for a given basis?