Assess students' ability to recall and state the spectral theorem for bounded self-adjoint operators on Hilbert spaces: include the main formulations (finite-dimensional diagonalization, representation via a projection-valued measure/resolution of the identity, and the Borel functional calculus), key consequences (real spectrum, spectral decomposition, relationship to compact operators), and canonical examples (multiplication operator on L^2, compact self-adjoint operators with orthonormal eigenbases, and finite self-adjoint matrices). Also require naming types of spectrum (point vs continuous) and basic properties of the spectral measure.