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The mathematical concept of a Hilbert space generalizes the notion of Euclidean space. It extends the methods of Euclidean geometry and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces of any finite or infinite dimension. A Hilbert space is an abstract vector space, and it has the additional structure of an inner…
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| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Hilbert space | is a | abstract vector space | 0.90 | text |
| Hilbert space | is a | Euclidean vector space consisting of three-dimensional vectors | 0.90 | text |
| Hilbert space | is a | real or complex inner product space that is also a complete metric space with respect to the distance function induced by the inner product.To say that a complex vector space H… | 0.90 | text |
| Hilbert space | is a | space of random variables on a given probability space | 0.90 | text |
| Hilbert space | is a | sequence x 1 | 0.90 | text |
| Hilbert space | is a | uniformly convex Banach space.Best approximationThis subsection employs the Hilbert projection theorem | 0.90 | text |
| Hilbert space | is a | uniformly convex Banach space | 0.90 | text |
| Hilbert space | is a | finite-dimensional vector space.Completeness of an orthonormal system of vectors of a Hilbert space can be equivalently restated as | 0.90 | text |
| Hermann Weyl | instance of | Although other mathematicians | 0.80 | text |
| Norbert Wiener had already studied particular Hilbert spaces in great detail | instance of | Although other mathematicians | 0.80 | text |
| often from a physically motivated point of view | instance of | Although other mathematicians | 0.80 | text |
| von Neumann gave the first complete | instance of | Although other mathematicians | 0.80 | text |
These clusters group vocabulary that occurs around closely connected concepts in the source material.
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