- 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.
Hilbert space
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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
Projective Hilbert space — In mathematics and the foundations of quantum mechanics, the projective Hilbert space P ( H ) of a complex Hilbert space H is the set of equivalence classes of vectors v in H , with v ne; 0, for the relation given by : v w when v = lambda; w with … Wikipedia
