For the Hilbert space-filling curve, see Hilbert curve.This article assumes some familiarity with analytic geometry and the concept of a limit. The article on vector spaces contains useful background, and the article on functional analysis is closely related. The mathematical concept of a Hilbert space, named after the David Hilbert, generalizes the notion of Euclidean space in a way that extends methods of vector algebra from the two-dimensional plane and three-dimensional space to infinite-dimensional spaces. In more formal terms, a Hilbert space is an inner product space — an abstract vector space in which distances and angles can be measured — which is "complete", meaning that if a sequence of vectors approaches a limit, then that limit is guaranteed to be in the space as well.
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