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Lecture
Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
This lecture covers the concept of orthonormal sequences in Hilbert spaces, explaining how they can be used to decompose elements into orthogonal components. It also delves into Bessel's inequality, Cauchy-Schwarz inequality, and the importance of separable Hilbert spaces. The instructor discusses the relationship between orthonormal bases and algebraic bases, the polarization identity, and the characterization of orthonormal bases. The lecture concludes with a detailed proof involving orthogonal complements and unique decompositions in Hilbert spaces.