Hilbert Space Theory 2.0 2003/01/15 2003/01/15 Phil Schniter schniter@ee.eng.ohio-state.edu Charlet Reedstrom charlet@rice.edu Phil Schniter schniter@ee.eng.ohio-state.edu Hilbert Space Theory review Hilbert spaces provide the mathematical foundation for signal processing theory. In this section we attempt to clearly define some key Hilbert space concepts like vectors, norms, inner products, subspaces, orthogonality, orthonormal bases, and projections. The intent is not to bury you in mathematics, but to familiarize you with the terminology, provide intuition, and leave you with a "lookup table" for future reference.