Search for "Hilbert space" in article titles:

1. Hilbert space: In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. A Hilbert space is a vector space equipped with an ... (Generalization of Euclidean space allowing infinite dimensions) [100%] 2022-09-12 [Hilbert space] [Linear algebra]...
2. Hilbert space: A vector space $ H $ over the field of complex (or real) numbers, together with a complex-valued (or real-valued) function $ ( x, y) $ defined on $ H \times H $, with the following properties: 1) $ ( x, x) = 0 $ if and only if ... (Mathematics) [100%] 2024-01-13
3. Hilbert space: In mathematics, Hilbert spaces (named for David Hilbert) allow generalizing the methods of linear algebra and calculus from the two-dimensional and three dimensional Euclidean spaces to spaces that may have an infinite dimension. A Hilbert space is a vector ... (Generalization of Euclidean space allowing infinite dimensions) [100%] 2021-12-23 [Hilbert space] [Linear algebra]...
4. Hilbert space: In mathematics, particularly in the branch known as functional analysis, a Hilbert space is a complete inner product space. As such, it is automatically also a Banach space. [100%] 2023-07-30
5. Reproducing-kernel Hilbert space: Let $H$ be a Hilbert space of functions defined on an abstract set $E$. Let $( f , g )$ denote the inner product and let $\| f \| = ( f , f ) ^ { 1 / 2 }$ be the norm in $H$. (Mathematics) [81%] 2023-10-17
6. Projective Hilbert space: In mathematics and the foundations of quantum mechanics, the projective Hilbert space \displaystyle{ P(H) }[/math] of a complex Hilbert space \displaystyle{ H }[/math] is the set of equivalence classes of non-zero vectors \displaystyle{ v }[/math] in \displaystyle{ H ... [81%] 2023-05-20 [Hilbert space]
7. Rigged Hilbert space: A Hilbert space $ \mathcal{H} $ containing a linear, everywhere-dense subset $ \Phi \subseteq \mathcal{H} $, on which the structure of a topological vector space is defined, such that the imbedding is continuous. This imbedding generates a continuous imbedding of the ... (Mathematics) [81%] 2023-10-19
8. Projective Hilbert space: In mathematics and the foundations of quantum mechanics, the projective Hilbert space P ( H ) {\displaystyle P(H)} of a complex Hilbert space H {\displaystyle H} is the set of equivalence classes of non-zero vectors v {\displaystyle v} in H ... [81%] 2023-03-22 [Hilbert space]
9. Reproducing kernel Hilbert space: In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Roughly speaking, this means that if two functions \displaystyle{ f }[/math] and ... [70%] 2023-07-12 [Hilbert space]
10. Reproducing kernel Hilbert space: In functional analysis, a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Specifically, a Hilbert space H {\displaystyle H} of functions from a set X {\displaystyle X} (to ... (In functional analysis, a Hilbert space) [70%] 2024-10-31 [Hilbert spaces]
11. Hilbert space with an indefinite metric: A Hilbert space $ E $ over the field of complex numbers endowed with a continuous bilinear (more exactly, sesquilinear) form $ G $ that is not, generally speaking, positive definite. The form $ G $ is often referred to as the $ G $- metric. (Mathematics) [57%] 2023-05-29
12. Hilbert Space: Hilbert space is an inner product space that is also a complete metric space. A Hilbert space is always a Banach space, but the converse need not hold. [100%] 2023-03-02 [Mathematics]
13. Semi-Hilbert space: In mathematics, a semi-Hilbert space is a generalization of a Hilbert space in functional analysis, in which, roughly speaking, the inner product is required only to be positive semi-definite rather than positive definite, so that it gives rise ... [81%] 2023-08-29 [Topological vector spaces]
14. Pre-Hilbert space: A vector space $ E $ over the field of complex or real numbers equipped with a scalar product $ E \times E \rightarrow \mathbf C $, $ x \times y \rightarrow ( x , y ) $, satisfying the following conditions: 1) $ ( x + y , z ) = ( x , z ) + ( y ... (Mathematics) [81%] 2023-09-17