Hilbert space - Definition. Was ist Hilbert space
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Was (wer) ist Hilbert space - definition


Hilbert space         
  • billiard]] ball in the [[Bunimovich stadium]] is described by an ergodic [[dynamical system]].
  • 1=AC<sup>2</sup> + BD<sup>2</sup> = 2(AB<sup>2</sup> + AD<sup>2</sup>)}}. In words, the sum of the squares of the diagonals is twice the sum of the squares of any two adjacent sides.
  • well-defined]] net displacement (in orange).
  • energy]].
  • harmonic series]].
  • [[Spherical harmonics]], an orthonormal basis for the Hilbert space of square-integrable functions on the sphere, shown graphed along the radial direction
  • [[David Hilbert]]
  • Superposition of sinusoidal wave basis functions (bottom) to form a sawtooth wave (top)
  • none
INNER PRODUCT SPACE THAT IS METRICALLY COMPLETE; A BANACH SPACE WHOSE NORM INDUCES AN INNER PRODUCT (FOLLOWS THE PARALLELOGRAM IDENTITY)
Linear Algebra/Hilbert Spaces; Complex Hilbert space; Hilbert spaces; Hilbert spaces and Fourier analysis; Separable Hilbert space; Complete inner product space; Hilbert Space; Hilbert space dimension; Draft:Xu–Zikatanov identity; Square-summable sequence; ℓ2 space; ℓ2
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 inner product which defines a distance function for which it is a complete metric space.
Hilbert space         
  • billiard]] ball in the [[Bunimovich stadium]] is described by an ergodic [[dynamical system]].
  • 1=AC<sup>2</sup> + BD<sup>2</sup> = 2(AB<sup>2</sup> + AD<sup>2</sup>)}}. In words, the sum of the squares of the diagonals is twice the sum of the squares of any two adjacent sides.
  • well-defined]] net displacement (in orange).
  • energy]].
  • harmonic series]].
  • [[Spherical harmonics]], an orthonormal basis for the Hilbert space of square-integrable functions on the sphere, shown graphed along the radial direction
  • [[David Hilbert]]
  • Superposition of sinusoidal wave basis functions (bottom) to form a sawtooth wave (top)
  • none
INNER PRODUCT SPACE THAT IS METRICALLY COMPLETE; A BANACH SPACE WHOSE NORM INDUCES AN INNER PRODUCT (FOLLOWS THE PARALLELOGRAM IDENTITY)
Linear Algebra/Hilbert Spaces; Complex Hilbert space; Hilbert spaces; Hilbert spaces and Fourier analysis; Separable Hilbert space; Complete inner product space; Hilbert Space; Hilbert space dimension; Draft:Xu–Zikatanov identity; Square-summable sequence; ℓ2 space; ℓ2
¦ noun Mathematics an infinite-dimensional analogue of Euclidean space.
Origin
early 20th cent.: named after the German mathematician David Hilbert.
Rigged Hilbert space         
HILBERT SPACE EQUIPPED WITH A DENSE SUBSPACE THAT CARRIES (IN ADDITION TO THE SUBSPACE TOPOLOGY) A FINER TOPOLOGY SUCH THAT THE INCLUSION MAP IS CONTINUOUS
Generalized eigenspaces of unbounded continuous operators; Generalized eigenspaces of unbounded operators; Generalized eigenfunction; Generalised eigenfunction; Gelfand triple; Nested Hilbert space; Equipped Hilbert space; Rigged hilbert space; Banach Gelfand triple; (Banach) Gelfand triple
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 spectral theory in the broad sense.