Two matrices which are unitarily equivalent are also similar. The family of Hermitian matrices is a proper subset of matrices that are unitarily diagonalizable. One can show that is normal if and only if it is unitarily diagonalizable. "A" and "B" are unitarily equivalent. The spectral theorem says that every normal matrix is unitarily equivalent to some diagonal matrix. For example, the spectral theorem for normal matrices states every normal matrix is unitarily diagonalizable. To give an example, every constant-coefficient differential operator is unitarily equivalent to a multiplication operator. If two normal operators "M" and "N" are similar, then they are unitarily equivalent. Thus "G" acts unitarily on "H" on the right. In other words, a compact self-adjoint operator can be unitarily diagonalized.