[[Functional analysis MOC]]
# Hilbert space

A **Hilbert space** $(H, \langle \cdot|\cdot \rangle)$ is an [[inner product space]] that is [[Complete metric space|complete]] under its induced norm, #m/def/anal/fun
hence it is a [[Banach space]].

## Properties

- [[Nearest point of a convex subset of a Hilbert space]]

## Examples

- [[L2 space]]

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