Hilbert space
noun Etymology: David Hilbert Date: 1911 a vector space for which a scalar product is defined and in which every Cauchy sequence composed of elements in the space converges to a limit in the space

New Collegiate Dictionary. 2001.

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  • Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   Wikipedia

  • Hilbert space — Math. a complete infinite dimensional vector space on which an inner product is defined. [1935 40; named after D. HILBERT] * * * ▪ mathematics       in mathematics, an example of an infinite dimensional space that had a major impact in analysis… …   Universalium

  • Hilbert space — noun A generalized Euclidean space in which mathematical functions take the place of points; crucial to the understanding of quantum mechanics and other applications. See Also: linear algebra, vector space, inner product space, Banach space, pre… …   Wiktionary

  • Hilbert space — Hilberto erdvė statusas T sritis fizika atitikmenys: angl. Hilbert space vok. Hilbert Raum, m rus. гильбертово пространство, n pranc. espace de Hilbert, m; espace hilbertien, m …   Fizikos terminų žodynas

  • Hilbert space — noun Mathematics an infinite dimensional analogue of Euclidean space. Origin early 20th cent.: named after the German mathematician David Hilbert …   English new terms dictionary

  • Hilbert space — noun a metric space that is linear and complete and (usually) infinite dimensional • Hypernyms: ↑metric space …   Useful english dictionary

  • Compact operator on Hilbert space — In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… …   Wikipedia

  • Rigged Hilbert space — In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution and square integrable aspects of functional analysis. Such spaces were introduced to study… …   Wikipedia

  • Reproducing kernel Hilbert space — In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space is a Hilbert space of functions in which pointwise evaluation is a continuous linear functional. Equivalently, they are spaces that can be defined by reproducing …   Wikipedia

  • Weak convergence (Hilbert space) — In mathematics, weak convergence is a type of convergence of a sequence of points in a Hilbert space (and, more generally, in a Banach space). DefinitionA sequence of points (x n) in a Hilbert space H , with n an integer, is said to converge… …   Wikipedia

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