Summary of contents: projection and orthogonal complement; infinite-dimensional Pythagoras' theorem; open and closed sets; proof that a closed subset of a complete metric space is complete; a closed linear subspace of a Hilbert space is a sub-Hilbert space; proof that the orthogonal complement of a linear subspace is a closed linear subspace; orthogonal projector; proof of properties of orthogonal projectors; Riesz representation theorem with proof; Riesz map; critical discussion of Dirac's bra-ket notation.
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