Google search-bar gives the definition of Hermitian as:
Hermitian: denoting or relating to a matrix in which those pairs of elements that are symmetrically placed with respect to the principal diagonal are complex conjugates
I have thought that Hermitian was synonymous with "real", meaning, if the matrix (A, for example) is Hermitian then that means there are no complex values in the matrix. I also believe it means the complex conjugate of the matrix is equal to the matrix like so: $$A = A^\dagger.$$
However, there also exist Hermitian functions (which are complex?!) and the Hermitian operator (does not have to be real). Could someone please tell me what does the word "Hermitian" mean and what are the differences between the three: Hermitian matrix, Hermitian function, and Hermitian Operator? I am confused.
(PS: Please feel free to correct me if I have tagged this question incorrectly.)