Are Hermitian Operators Self Adjoint?

Are Hermitian Operators Self Adjoint? There is also a subtlety, that is, for every hermitian operator, you can construct an extension of this operator, which is self-adjoint. Are all Hermitian matrices self-adjoint? Every self-adjoint matrix is a normal matrix. The sum or difference of any two Hermitian matrices is Hermitian. Actually, a linear combination of