Liouville's theorem | Chinese remainder theorem | Shannon–Hartley theorem | Quillen–Suslin theorem | Nyquist–Shannon sampling theorem | Hahn–Banach theorem | Frölicher spectral sequence | Fermat's Last Theorem | Buckingham π theorem | Thue–Siegel–Roth theorem | Szemerédi's theorem | Schottky's theorem | Riemann-Roch theorem | Pythagorean theorem | Nash embedding theorem | Müntz–Szász theorem | Malgrange–Ehrenpreis theorem | Kleene fixed-point theorem | Kakutani fixed-point theorem | Gauss–Bonnet theorem | Doob's martingale convergence theorem | Dirichlet's theorem on arithmetic progressions | Denjoy theorem | Birch's theorem | Wilkie's theorem | Wick's theorem | Whitney extension theorem | Weierstrass theorem | Wedderburn's little theorem | Vietoris–Begle mapping theorem |
This is the spectral theorem in mathematics, and in a finite state space it is just a statement of the completeness of the eigenvectors of a Hermitian matrix.