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Hilbert space

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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Orthonormal bases

Orthogonal complements and projections

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Hilbert space

Nodes379
Edges378
Triples232
Avg. degree1.99
Density0.005277
Components1

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Hilbert space

Top relations

related to Sobolev spaces · 16
Hilbert space → Banach, Because, Df, Euclidean, For, Hilbert, Hs, Hölder, L2, Omega, Rn, Sobolev, The, These, They, Ws
related to Partial differential equations · 14
Hilbert space → An, Dirichlet, For, Galerkin, Hilbert, Lax, Many, Milgram, Omega, Poisson, R2, Sobolev, The, This
see also · 13
Hilbert space → Construction, David HilbertLocally, Fundamental, Generalization, Hilbert, Manifold, Mathematical, Mathematics, Non-linear, On, Space, Topologies, Type
related to Ergodic theory · 11
Hilbert space → An, As, Hamiltonian, Hilbert, In, L2, Liouville's, More, Omega, The, Tt
related to Bounded operators · 10
Hilbert space → Ax, Conversely, For, H1, H2, Hilbert, Riesz, The, This, When
related to Probability theory · 10
Hilbert space → Equivalently, Here, Hilbert, If, In, Omega, Suppose, The, Thus, X-E
related to history · 9
Hilbert space → David Hilbert, Erhard Schmidt's, Euclidean, Functions, Hilbert, In, Other, Prior, The
related to Separable spaces · 9
Hilbert space → All, Along, By, Dirac, For, Hilbert, Neumann, Separability, Zorn's
related to Sturm–Liouville theory · 9
Hilbert space → For, Furthermore, Green's, Hilbert, In, Liouville, Robin, Sturm, The
related to Unbounded operators · 9
Hilbert space → An, By, Hilbert, If, In, Operators, The, Unbounded, Unlike

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Important terminology

space hilbert displaystyle product linear orthogonal spaces operator operators theorem functions sum langle rangle inner defined bounded function one also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hilbert spaceis aabstract vector space0.90text
Hilbert spaceis aEuclidean vector space consisting of three-dimensional vectors0.90text
Hilbert spaceis areal 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…0.90text
Hilbert spaceis aspace of random variables on a given probability space0.90text
Hilbert spaceis asequence x 10.90text
Hilbert spaceis auniformly convex Banach space.Best approximationThis subsection employs the Hilbert projection theorem0.90text
Hilbert spaceis auniformly convex Banach space0.90text
Hilbert spaceis afinite-dimensional vector space.Completeness of an orthonormal system of vectors of a Hilbert space can be equivalently restated as0.90text
Hermann Weylinstance ofAlthough other mathematicians0.80text
Norbert Wiener had already studied particular Hilbert spaces in great detailinstance ofAlthough other mathematicians0.80text
often from a physically motivated point of viewinstance ofAlthough other mathematicians0.80text
von Neumann gave the first completeinstance ofAlthough other mathematicians0.80text

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