As noted above, the spectral theorem applies only to self-adjoint operators, and not in general to symmetric operators. Nevertheless, we can at this point give a simple example of a symmetric operator that has an orthonormal basis of eigenvectors. (This operator is actually "essentially self-adjoint.") The operator "A" below can be seen to have a compact inverse, meaning that the corresponding differential equation "Af" = "g" is solved by some integral, therefore compact, operator "G". The compact symmetric operator "G" then has a countable family of eigenvectors which are complete in . The same can then be said for "A".